How to punish this opening ?

First off, quit trying to "punish" an opening.  The opening serves one purpose, to get to a playable middle game.  You only punish openings when you opponent plays bad openings. 

If you think that "Hedgehog opening" refers to double fianchetto you might want to check it:

Exaggeration and now assumptions.  No, there is not necessarily double fianchetto in the Hedgehog.  The reference to it is that a good plan of attack against it is exploiting an advantage in space.

  Nowhere in my posts do I write anything other than playing opposite a double fianchetto within the first 4 moves there is a plan of attack involving advantage in space.

Try asking questions.  Stop leaping before you look.

I_Am_Second said it best, "...quit trying to "punish" an opening.  The opening serves one purpose, to get to a playable middle game.  You only punish openings when you opponent plays bad openings..." 

Well the OP is a beginner, in other words, one who has very little, if any, experience at all in dealing with any opening...he just seems to be most flustered when White opens with a double fianchetto. I've gotten my ass handed to me when my opponent played that as White, and I later discovered he gave one of our strongest players a draw with that same opening! I_Am_Second is basically spot on.

So the point being, if you understand something well and use it, it can be powerful indeed.

White first moves aim to get a solid position instead to search for an opening advantage. So you cannot "punish". That said consider what white is attempring to do. Finchettoing bishops hes aimingfor the long diagonals, so you should try to control & block the center to make those bishops "less usable".

an example:

black is fine and white too. The result of the game dephend on how good are both the players.

Obviously this is just an example of the load of reasonable lines. just follow some ideas:

* if opponent is fianchettoing its a good idea to block the diagonal with a pawn and try to bkock the center as much as possible.

* if opponent castle where a bishop is fianchettoed, its a good idea to exchange the bishops ( as in the diagram aiming for Bh3 )

* consider a pawn storm kingside. g3 weackens the wans strusture so coudl eb a good idea. to casle opposite dise and harras with pawns. just be aware that white will do the same queen side, so be sure that your pawn arrives first.

Those are justy my guidelines, but you should consider specific opportunities/threats depending on the position. Also consider that i'm not a master, its just what my ( poor) skills suggest me to do.

I play the Petroff Defence as Black whenever I feel like it, and I can get pretty badly "punished" at times!

I'll have a go at answering your question.

Your friend's idea disregards one of the well established opening principles. That principle says that it is generally better to develop knights before bishops. Why is that? It is because knights take longer to move from one side of the board to the other than other pieces. It makes good sense to give a little bit of priority to getting your knights started out so as to be sure that when the pawns and pieces start coming into contact the knights are not too far away to exert any influence.

How can you exploit the fact that after four moves both of white's knights are still firmly at home? I do not have an answer to that question which I can translate for you into a set series of moves (or rather I am too lazy to do so) but I can suggest that you focus on getting your own knights out and also focus on making some moves which aim to limit your friend's ability easily to develop his knights when he, belatedly, gets around to doing so. One idea that occurs to me is to target the c3 square. Perhaps you could exploit his passivity by seeking a pawn structure in which your pawns occupy the d4, e5 and f6 squares. That will blunt his black squared bishop and also give you a considerable space advantage. It will also deny his king side knight the square on which it is most naturally developed, c3.

If you thought that idea to be appealing you need to find a good square for your own queen side knight - almost certainly e7 - and it would almost certainly also make sense to advance your c pawn to c5 before getting your king side knight out to c6.  If you succeeded in all these endeavours your space advantage would be very great and I think your friend might be in difficulties. However, of course, he will be making moves while you are advancing all these pawns and there are countless variations some of which would favour you and some him.

You would, in fact, be exploring something which was explored extensively by top players in the earlier part of the twentieth century. Classical chess players had believed it essential to occupy the centre with pawns so as to secure sufficient influence there. But a school came along called the hypermodern players who believed that you could allow your opponent to occupy the centre and then gain advantage by working to undermine that centre. Without, perhaps, knowing it your friend belongs to that school. So, in the cut and thrust of the opening the issue would be whether your occupation of the centre would swing the game in your favour or whether your friend could gain an advantage by undermining your centre.

I will say one last thing. It is understandable for you to be interested in specific series of moves at the beginning of games. The point I would make to you however is that before starting to look at highly specific moves you will do well to reach a decently robust grasp of the opening principles. You will find any number of good expositions of those principles online and I suggest you read over two or three and then simply try to follow them in a few dozen games to see how the principles can be seen to influence play. That will help your game a great deal more than devising a specific answer to your friend's hypermodern idea. :)

I will say it's spectacular when one has so much time that they can afford to spend it on writing all that! Perhaps a career in journalism?

I'm currently watching one of Yasser Seirawan's lectures for the St. Louis chess club and it's relative to the question.

He says that in the opening you want....

1. To gain your fair share of the center.

2. development of your pieces

3. safe King

4. Sound pawn structure

That's all you really want. After that you just play chess....

If your friend plays like you posted, you are sure to get a fair share of the center. And if you concentrate on development you should easily develop even with or quicker that your friend. Castle quickly and you'll have a safe king. And don't wildly throw your pawns away.... You should have a very good start to the game. Then it's a matter of playing good chess.

1. To gain your fair share of the center - Are you talking about the center, or the big center?

2. development of your pieces - development where?

3. safe King

4. Sound pawn structure - What sound pawn structure are you aiming for?

1. There's always exceptions!!! In an opening like the Hippo, which is an opening very similar to the one that OP wants to "punish" where the Bishops are fianchettoed on both flanks, Black purposely gives White the center, and he depends on all of White's replies. I noticed that IM Martin says (in his book about that opening) that when White plays an early Bc4 is to answer with ...a6 followed by ...b5 to target that Bishop.

2. Development of the pieces: Knights also get placed on the second rank...unless if White's replies demand you place them elsewhere.

3. Safe King - mostly he is castled short. Very rarely you leave him in the center or castle long.

4. IMO, playing an opening where I'm giving White the center I will want to block it, as I noticed that usually (and I use that term lightly) handles well...but of course I still need more practice with such an unorthadox opening, especially being at the rating I'm at now.

The idea behind the double-fianchetto is along the lines of the hyper-modern school of thought in chess, where a player invites his opponent to occupy the center, with the intentions to show that the opponents occupied center (usually by pawns) is more a liability than an advantage.  That's sort of the gist of it.  I confess that I'm not all that up to date on hyper-modern theory, so if you want more information on it, look up the appropriate information.  But, what I'm suggesting, is simply to play into his ideas.  Take space in the center with some pawns, back them up with pieces (as actively as you are capable of) and slowly push forward, per se.

One good idea against double fianchetto is to 'kill' one of the bishops. For example, if we know that black wants to play a double fianchetto with Bishop b7 and g7, we can 'kill' the bishop on b7 with c4 and d4-d5. of course, we can't do this if black manages to play c5 before white plays d4. 

we can also try to play d3 and e4 restricting the bishop on b7. Or sometimes we can play c3, d4, e3 to kill the bishop on g7.