Some years ago Bobby Fischer suggested what he called a 'A Bust To The King's Gambit' in the American Chess Quarterly (1962-63). Click hear to see the article.
You may only be rarely confronted with this variation, but the King's Gambit may be met often at club level, so, following I give some possible ideas for White.
1.e4 e5 2.f4 exf4 3.Nf3
Fischer's idea is that Black wants to defend the gambit pawn by ...g5 while keeping out White's knight from the attacking square e5. For instance, if at once 3...g5 4.h4 g4 5.Ne5 and White has enough for the pawn.
3...d6 This was called by Fischer 'a high-class waiting move.'
Fischer gives two main lines after...d6.
1) 4.d4 g5 5.h4 g4 6.Ng5 f6! 7.Nh3 gxh3 8.Qh5+ Kd7 9.Bxf4 Qe8 10.Qg4+ Kd8 and White has no real attack for the sacrificed piece.
2) 4.Bc4 h6! 5.d4 g5 6.0-0 Bg7 7.c3 Nc6 8.g3 g4 9.Nh4 f3 when if 10.Qb3 Qe7 11.Bf4 Nf6 12.Nf5 Bxf5 13.exf5 0-0 with a good game for Black. If then 14.Qxb7 Na5 15.Qa6 Nxc4 16.Qxc4 Rab8 material is level but Black holds the initiative.
White can try to postpone pawn to d4 in favour of breaking up the black pawn chain, but 4.Bc4 h6! 5.0-0 g5 6.g3 Bh3 should still favour Black.
A rarely played suggestion for White by Robert G. Wade goes as follows 4.d3 g5 5.h4 g4 6.Ng1 Bh6 7.Bd2 Nc6 8.Nc3 Be6 9.Nce2 White's overall plan has been to hold back his centre in order to avoid premature pawn exchanges.