I remember seeing a video a while back, which introduces this sub-variation to spice things up and to surprise black when they expect a dull draw game.
I don't think it has a name, and I can't quite remember the moves now, so it's hard to search in an opening database.
The Exchange Variation might lead to early opposite-side castling with prospects of mutual pawn storms:
[fen ""]
1.e4 e6 2.d4 d5 3.exd5 exd5 4.Bd3 Nc6 5.Nf3 Bg4 6.c3 Qd7 7.O-O O-O-O.
Now if 8.Nbd2 Bd6 9.Re1 Nge7 10.b4, Euwe advised: 10...Rde8 to allow retreating the knight in case of b5. The line above is from a general opening book by Panov. In this example, White is slightly better and can be first to develop a dangerous attack. So, Black is probably better off with simple: 6... Qf6 7.Nbd2 Qe6+ 8. Be2 Bd6.
It's almost impossible to make it work with, say, White castling long and Black short unless Black is a low rated player/amateur. However, opposite castling may occur later in the opening but usually it doesn't.
Also, some ideas might be possible with 3.Nc3 Bb4 (the Winawer Variation) but both sides should be willing or we are highly unlikely to have opposite-side castling. Below is an example of such variation where White castles long as the OP wanted:
[fen ""]
1. e4 e6 2.d4 d5 3.Nc3 Bb4 4.Ne2 dxe4 5.a3 Be7 6.Nxe4 Nc6 7. Be3 Nf6 8. Qd3 O-O 9. O-O-O a6 10. h4 b5.
Most of the time there won't be any opposite side castling even if both sides want it, unless players are amateurs.