g7
but then probably Bd4 Kxd4 e5 Kxe5 Ne7?

That's right. Now white should rove the knight away.

1. Nf8 e5
2. g7 Ne7
3. Ng6 +-

@blob
1.Nf8 Bd4+

bob: tablebase shows it's drawish
blob: same defence here - 1.Nf8 Bd4 2. Kxd4 e5 3.Kxe5 Ne7 - draw

Martas: tablebases spoil the fun here. Prove to me its a draw, without looking up the answers. 1 Nf8 Nd6 2 g7 Bd4+ looks clearer to me, anyway.
So let's after all start with 1 g7 Bd4+ 2 Kxd4 e5+ 3 Kxe5 Ne7 4 Kf6 Ng8+ 5 Kf7 Nh6+. So far, all straightforward. Now my first try is 6 Ke8 b5 7 Nf8 b4 8 Ng6+ Kg5 9 Ne7 b4 10 Nc6 b3 11 Nd8 b2 12 Nf7+, but there is no win after Kf4 13 Nxh6 b1Q 14 g8Q Qb8+. Not easy without a board!

And that's the problem with analyzing without a board: pawns are getting either faster or slower... Checking it, I see black is playing b4 twice in my line. Happens to me in regular games too, lately. The price of passing 50, I guess.

And now I see there is a much easier way to reach f7: 9 Nh8, but it's still a draw after Kf6 10 Kf8 b3 11 Nf7 b2. Anyone taking over? I'm supposed to make some money now...

a direct way to win: 1-g7 Bd4+2-K.d4 e5+3R.e5 Ne7 4-Kf6 Ng8+5-Kf7 Nh6 6-Kg6 Ng87-Nf68-Ne7+9-Kh7(Kf7? and then ..Nf5) b5(Kg5?) 10-Kh8 +-

Pedram, I found that too, but what after 10 ... b4 11 Nd5 b3 12 Nxe7 b2 13 Nf5+ Kh5 14 g8Q b1Q? For instance: 15 Qh7+ Kg5 16 Qh4+ Kg6 17 Qh6+ Kf7 18 Qh7+ Kf6 and I don't see a way for white to make progress. By the way, you can get the same position with a black pawn on e5, by playing 3 Kd5 Ne7+ 4 Ke6 Ng8 5 Kf7, but I don't see what's the difference.

Amen, I've seen the light!
White should absolutely not take the pawn on move 3, and continue the line 14 Qh7+ Kg5 15 Qh4+ Kg6 16 Qh6+ Kf7 with 17 Qg7+ Ke6 18 Qg6+! and I leave the rest to those willing to rack their brains - there is a quite move at the end.

quite a quiet move, I mean