Thanks Paul... I meant Be6 on black's 3rd move.
Queen's Gambit Accepted

Just don't fall for this trap in this Slav/QGA hybrid type thing. Even GMs have fallen for it, as shown by databases.

That's entirely different! 3...Be6 is an annoying looking move, but I think you should be fine. After 4.Nc3 c6 5.Nf3 b5 it sems to me that Black is falling farther behind in development and creating a weak queen side. After something like 6.a4 b4 7.Ne2 You seem to be OK. Either one of Black's queenside pawns will fall, or you will be way ahead in development
Except for the thoughtful post above, most of the suggestions in this thread are just a bit silly. Mostly a collection of engine suggestions (at best), and that probably includes 3)...Be6.
Simply buy James Rizzitano, "How to Beat 1)d4," (Gambit 2005) and (maybe) learn the opening from both sides. It's a great classical opening.
The QGA was played by all of the first 14 World Champions, so there's already plenty of theory developed (and books "in print") for you to study. If you really want to learn it, then get with the program.
An older book, by Cafferty and Hooper, "Complete Defense to 1)d4" (Pergamon, 1981) has a chapter (pps. 63-65) devoted partly to the 3)...Be6 move, covering roughly the first 15 moves for both sides.
Learning a move here, and a move there, will just land you in hot water. Why bother with that?
Or you can put everything on Rybka, and give up thinking altogether. Many people do just that.
Good luck with whatever path you choose.
If black plays 2...Be6 White can play 3.Na3! and there is no way Black can save the c4 pawn.3...Qd5 is not a good idea because of 4.Bxc4.

3 ...Be6 has been played by GM Flear, IM Pitl, and FM Gelazonia against master class opposition in the last five years, so it isn't unheard of.
Black can fight for the pawn, but White has more than enough play to compensate for it. Concentrate on development, 4 Nc3 c6 5 Nf3 b5 6 Be2 Nf6 7 0-0 and White is getting very comfortable while Black is still awkwardly placed.
Another thoughful post for the OP appears above. All good suggestions.
The 3)...Be6 move is the "Winawer Variation" (Ch. 6, in Cafferty and Hooper). Not really covered in Rizzitano's book.
If you insist on getting the pawn back immediately, simply play some version of the the (forcing) "Manneheim Variation", (Ch. 10 in Cafferty, Ch. 3 in Rizzitano) with 4) Qa5+, and just take the black pawn on c4 with your Bishhop. This keeps the game simple, but probably gives Black equality much sooner.
In your example given above, Black is effectively "choosing the opening" (QGA), and choosing one of the offbeat variations within the defense, in order to put you onto unfamiliar territory that your opponent has probably studied.
So perhaps force him into some version of the Mannheim Variation, with 4) Qa5+ (assuming that's kosher for white), or get prepared to play on your opponents already studied ground, the slightly off beat, but still playable 3)...Be6 Winawer.
Conversely, you can play a reversed black system with the white pieces (like a reversed Slav, or a reversed Queen's Indian Defense (QID, i.e. Larsen Attack) and presto, you have put your opponent onto "your ground," so to speak. And that way, you don't need to study the QGA at all.
Earlier, there was an entire thread on Chess.com devoted to whether Black can take the pawn on c4 and hold onto it. Massive amounts of Blah, Blah, Blah, and clash of egos.
In this thread, the best practical recommendations came from @Gottlieb and @Estragon. They know what they are talking about.
Good luck with it.
Okay, I'm white and it goes
1. d4 d5 2. c4 dxc4 3. e3 Be6
What's my best play here?
I played Nd2, he played b5.
I start thinking about getting my Queen to f3 somehow, but see he can just block with his bishop on d5 and is guarded by his Queen, so that's dead for now.
I played a4 (should I have played something else?) and was still thinking about a way to get my Queen to f3, after getting his bishop to move.
I"m just trying to explore all the Queen's Gambit moves here and he threw me a new one with his Be6 move. (Yes, I am practicing on my middle game and end game too.
) ( I asked a man around 60 years old, while we were playing poker, who said he used to be a 2050 player but had quit 35 years ago, and he said in Queen's Gambit accepted, that it was easy to pick up that black pawn and still have great development, but that was all he said, no examples)
Thanks for any help, especially from 1700+ players.