Not all Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+) players open with the Jerome every game. Some add variety to their play, even venturing the "Quiet Game", as can be seen below.
However, when challenged, they can quickly become Jerome-ish.
FlyingInsect762 - Filou1962
10 0, lichess.org, 2022
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.c3
White - who has 3 dozen games in The Database - is looking for a standard Giuoco Piano this time.
Black tries to cross this up, however.
4...Na5
Looking to win the "minor exchange", trading his Knight for his opponent's Bishop.
The database has 51 games with this move. White scores 75%.
The earliest example of 4...Na5 that I have been able to find is Najdorf - Avino, blindfold simul, San Pablo, 1947 (1-0, 13).
White can now retreat his Bishop, or he can protect it with 5.Nxe5, although the latter move reduces his advantage to about 2/3 of a pawn, after 5...Nxc4 6.Nxc4 d5.
5.Bxf7+
You know that you are in trouble when this is Stockfish's choice, too.
The earliest example of Bxf7+ that I have been able to find in this position is Ubeda - Lopez, Santiago, 1992 (1-0, 32).
However, the Scotch Gambit has seen the ...Na5 plus Bxf7+ pairing much earlier, e.g. 1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Bc4 Na5 5.Bxf7+ in Schnitzler - Thieler, Duesseldorf, 1866 (1-0, 10).
5...Kxf7
It is interesting to compare the current position with the one that arises after 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ Kxf7 5.c3, when 5...Na5 would be a useless continuation. White's advantage in this game is due, in part, to Black's lost tempo.
6.Nxe5+
Continuing Jerome style.
Instead, White could take advantage of Black' awkwardly placed pieces with 6.b4!?
Stockfish 16.1's first response (38 ply) is 6...Nc6 7.bxc5 d5 8.cxd6 cxd6 9.d4 and White is better.
A different approach (since his is going to lose a piece, anyhow) is 6...Nf6 7.Nxe5+ Kf8 8.bxa5 Nxe4 9.d4 which is again better for the first player.
Finally, if Black meets 6.b4!? with 6...Bxf2+, then 7.Kxf2 Nc6 8.b5 Nce7 9.Nxe5+ will again keep White on top.
6...Ke6
Black's King advances boldly, but he would do better to retreat to f8, when White would have to mobilize his "Jerome pawns" to keep things even, i.e. 6...Kf8 7.b4 Bd6 8.bxa5 Bxd5 9.d4 Bf6 10.e5 Be7 11.0-0.7.d4 Bd6
It is amusing to consider the stronger 7...Nf6, ignoring the attack on his Bishop and, instead, attacking White's e-pawn. The you-take-my-piece-I-take-your-piece would still play out after 8.dxc5 Kxe5 with 9.0-0, when Black's King is too exposed.
Instead, after 7...Nf6, the pawn fork 8.b4 would again cause problems for the defender. Then 8...d6 8.Nd3 Nc6 9.bxc5 Kf7 leads to a position that looks like it is becoming solid for the defender, but which Stockfish - appreciating the "Jerome pawns" - assesses as about 3 1/2 pawns better for White, whether he plays 10.cxd6 or 10.Nd2 or 10.f3.
The text allows White to quickly end the game.
8.Qg4+ Ke7 9.Qxg7+ Ke8 10.Qf7 checkmate