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Not my originality but i would like to share it with you all. An easy puzzle mate in 3.
Your puzzle is stupid there are many mates, one of which is way faster.

why does h4 work so well
Because black can't stop all the passed pawns. One of the four will be able to safely queen.
why does h4 work so well
Because black can't stop all the passed pawns. One of the four will be able to safely queen.
Exactly. If 1...Bxh4, then b8=Q+. And if, for example, 1.Kf1, then 1...Bb8 2.h4 Kxb5 3.h5 Kxa6 4.h6 Kxb7 5.h7 Be5. And this position is even better for black. So, immediately h4 is very important tempo, which allows white promote one of this pawns to a queen.
In solution after 4.h7 black can play 4...Be5, but the 5.h8=Q or 5.b8=Q is winning. So I didn't add this moves to the solution, because there are two possible ways to win at the move 5.