Two-Bishop Mate?

You'll get much more out of working it out yourself. It's not really very hard. Spend a Sunday afternoon on it, or play a few positions on https://syzygy-tables.info/ and take the lone king moves from the top of the list on the right.
But that's a bit slow. You want to push the king to a corner and leave him as little space as possible (but watch out for stalemate). The bishops on d3 and e3 are too far back at the start. They trap the king but they leave him a lot of space.
This leaves him less space.
Notice that because the bishops are on adjacent diagonals the king is trapped behind the light squared bishop's diagonal and you only have to walk your king into the same area up the diagonal to h4 and mate him. Try finishing it against the Syzygy tables or Stockfish or whatever. It shouldn't take more than 19 moves from any position if you get it right.

Spend the time and do it yourself. Chess dot com may even have (I don't know) a quick and easy method to set up any position you like, and then you can play an engine that operates at a "perfect play" level.
Once you do the two Bishops, then advance on, to try the Knight and a Bishop.
Both of these end-game theories are worth their price-of-admission, the work to slave over their mastery.
It used to be, in times of old, that you'd have to explore Fine's Basic Chess Endings, to do this research on your own, but engines (computers) allow you to take these exercises on, on your own.
Best of luck.
Presumably you've got the hang of it by now. If you start as in #7 it comes out faster but according to Nalimov I still lost at least one move somewhere. It should be mate in 15.
Edit: Worked second go. 4.Kf3 gets the king forward faster because if he replies 4...Kh5 you can switch corners as in the variation.

Idk an exact algorithm, but I've tested it against a bot and it worked for me. All I can remember is
#1: Close the king's squares and use the king to protect bishops.
#2 After it is on the edge, herd it into a corner.

httpshttps://www.chess.com/es/drills/practice/mate-con-pareja-de-alfiles-1://www.chess.com/es/drills/practice/mate-con-pareja-de-alfiles-1
It can give 404 error , try go to puzzle-> drills -> chekmates->two bishops

But that's a bit slow. You want to push the king to a corner and leave him as little space as possible (but watch out for stalemate). The bishops on d3 and e3 are too far back at the start. They trap the king but they leave him a lot of space.
This leaves him less space.
Notice that because the bishops are on adjacent diagonals the king is trapped behind the light squared bishop's diagonal and you only have to walk your king into the same area up the diagonal to h4 and mate him. Try finishing it against the Syzygy tables or Stockfish or whatever. It shouldn't take more than 19 moves from any position if you get it right.
Right !
It's about twelve years since I seriously practised this endgame, but I think the rule is not to lose a tempo except when it's necessary at the edge of the board to avoid stalemate or adjust the parity. On move 8 you can move the bishop pair forward by either 8.Bg5+ or B.e5 followed by 9.Bf5(+).

It's about twelve years since I seriously practised this endgame, but I think the rule is not to lose a tempo except when it's necessary at the edge of the board to avoid stalemate or adjust the parity. On move 8 you can move the bishop pair forward by either 8.Bg5+ or B.e5 followed by 9.Bf5(+).
I'm not sure that I've ever read anything on this checkmate. I taught myself how to play it in the 1970s without computer assistance. The solution I presented was played on my iPad in the early morning and not analyzed with a computer (until now).
Your suggested 8.Bg5+ and 8.Be5 are both superior to what I played and my suggested Bh2. Most of the perfect moves from that position, however, do lose a tempo. Maybe track down where you learned the "rule" and subject it to computer analysis. I used Hiarcs 12 for my analysis because it has access to the tablebases on my drive.
From the starting position it is mate in fifteen.
Every move that is not perfect is annotated with a move that is.
@Ziryab
Yes, you're right.
I also taught myself the ending but I beat you to it by a couple of decades.
About twelve years ago, after discovering EGTBs, I spent a whole weekend doing nothing but playing this endgame against Nalimov with the aim of not just mating but mating in the fewest moves. This was very successful at the time, but sadly I seem to have forgotten much of the technique in the interim. My "rule" was "remembered" from that session, but in fact it should be that it's not necessary to waste a move with a bishop until you reach the edge of the board rather than it's necessary not to waste a move with the bishop until you reach the edge of the board.
In fact it's more psychological than useful anyway. For example in #13 move 9 I automatically played the king to g6 even though it's going to f6. The reason was obviously just to avoid wasting a bishop move on the next move. It doesn't actually save anything. (OK the king is at the edge of the board at that point, but I still avoid the bishop waits out of habit.)
Incidentally there's something funny about the EGTBs. Presumably you added Bh2 yourself, but I checked with my local Nalimov and Bd3 is shown as optimal but missing from your Hiarcs 12 list. The Nalimov list agrees with the syzygy-tables.info list (as you would expect for this endgame) but the Lomonosov list is also missing Bg5+.

Hiarcs had Bd3; I failed to type it in.
That sounds like a weekend well spent. I play these positions against the computer frequently, and sometimes I labor to find the best move. Usually I aim for speed—instant moves with some degree of efficiency.
One night at the local chess club, a high school student and I practiced mating with a queen. He set his Chronos for 10 seconds each. We had a couple of stalemates, but we were both able to deliver checkmate in as little a five seconds elapsed time.