In this position:
White can mate with
cxd6# or gxf6# en passant, depending on whether black just moved d7-d5 to f7-f5. No other move is mate-in-one.
Observe that
Black couldn't have made any other move, since a one-space pawn move would start with White in check, and a King move would start from an impossible double check. This differs from other solutions that rely on the game being over by stalemate if en passant is impossible.
For completeness, we should ensure this position is reachable. Prior to Black's moving d7-d5 or f7-f5, White could have gone Ra8-c8 capturing black's Queen, which Black just moved there. There's not much constraint from here and plenty of slack for White's pawns to make enough captures to get into the needed files, so I hope I can get away with not providing a proof game.