With Black's e-pawn unstoppable, White must create some counter-play. Spotting the drawing mechanism should not be difficult, but making it work is very tricky indeed. The idea has to be based on Black's walled-in king, and a knight check on c5 must be part of it. There are two routes, via e4 or e6, and little apparently to choose between them.
So let's try 1. Nf6 e2 2. Ne4 e1=Q. Now White can force his pawn home with 3. Nc5+ Bxc5 4. d8=Q, but after Qe5+ he is still a piece behind and sure to lose. Another look should reveal the brighter idea: 4. d8=Q Bxd8 5. Nc5+ Kb6 6. Nd7+ with perpetual check on c5 and d7.
But instead of playing 4 . . . Bxd8, Black ruins everything with Qxe4] when 5. dxe4 Bxd8 is hopeless for White, and 5. Qxb6+ Kxb6 6. dxe4 d3 is just as bad.
Back from the losing board to the drawing board, we try the other route: 1. Nf8 e2 2. Ne6 e1=Q, but what difference does it make? 3. Nc5+ is the same as before, and 3. d8=Q is met by Qxe6]
Most solvers now run out of ideas. Yet there is one glorious move that saves the game. Looking at 4. Qxb6+ is easy, when 4 . . . Kxb6 loses to 5. dxe6 Kc6 6. Kxa7 Kd6 7. Kxb7 Kxe6 8. Kc6, but forcing oneself to look beyond 4. Qxb6+ Qxb6 is difficult. White is a queen behind for nothing to show for it.
Yet the quiet 5. Kc8]] forces a draw. Black must make a move. Only the queen can do so, and she has only one safe square. So it has to be 5 . . . Qd6 and the game is drawn by stalemate.