Quite some bishop maneuvering required here, but all fitting in a single and simple plan. The black squared bishop goes to g3, the king helps closing a box for the promoted queen at g4, and the white squared bishop creates tempi. Black's moves are pretty forced in this sequence:
1.e3 (not e4! see move 6) Kg1 2.Bh4 h1=Q 3.Bf2+ Kh2 4.Bg3+ Kg1 5.Kg4! closes the box for the black queen) Qh2 (what else?) 6.Be4! Qh1 7.Bd5 Kf1 8.Bc4+ Kg1 9.Be2! Qh2(again, what else?) 10.Bf3 Qh1 11.Be4 Kf1 12.Bd3+ Kg1 13.Bc4 Qh2 14.Bd5 Qh1 (otherwise white takes on h2 and g2 and wins with the pawn) 15.e4! (at last) Kf1 16.Bc4+ Kg1 17.e5 Qh2 18.Bd5 Qh1 19.e6 Qh2 20.Bxh2+ Kxh2 21.Bxg2 and the pawns do the job.