What's the best way to play against this line? (in the QGA)

That isn't refuting 3...e5, it is showing ideas white can use against this move.

I meant 'refuting' in the sense of 'gaining an advantage'

Yes, 3Nc3 a6 is probably the most promising line for black, but 3...e5 is quite ok.

Thanks for the link to GM Illingworth.

1.d4 d5 2.c4 dxc4 3.e3 e5 is a perfectly normal move. White should play 4.Bxc4 when after 4...exd4 5.exd4 we have a position which may even occur from French defense, exchange variation.

The late GM Yuri Razuvaev analyses this particular structure in an excellent old article, which is included in Dvoretsky's book "opening preparation" (out of print since ages, AFAIK). He rightly concludes that while it is close to equal, Black must be very careful- this is the type of IQP position that gives white good attacking chances. All that said, Razuvavev's article concentrates on the ...Nf6 and ...Be7 developing scheme, and the option of ...Bd6 is mentioned without analysis.

I do not like 3.e4, because white has to be prepared against several good moves after it- e.g. so far I do not know a way to show some sort of an advantage after 3...Nc6.

I have looked here at all three possible white replies (Nc3,Nbd2,Bc4) but none of them seems able to trouble black.

To return to topic though, could you still elaborate on why 3. ... e5 is a "bad" move for black (post #23)? How does white punish that move exactly?

Perhaps you could on 2....dxc4 is play 3. e4 instead. The central Variation avoids 3...e5 and let's you finish developing. Ultimately it is hard for Black to keep his pawn he has gotten by accepting the Gambit. I see this line of 3. e3 played to swindle Black into trying to hold the pawn and open his h1-a8 diagonal to a well timed Qf3 to pick up the Rook or the Bishop.

It doesn't 3...e5 is the classic response to 3e4 too.  3.e3 e5 is by no means unusual and any decent book on the Queen's Gambit accepted. The article mentioned by IM Pfren is one of the best ways to learn white's ideas.

the computer suggested