With Black's king having no flight squares, there are two natural ways of threatening mate: 1.Ng6 (threatening Nf8) and 1.Rf5 (threatening Nf4).
After 1.Ng6, Black can cover f8 by moving his bishop from d8. 1...Bc7 allows 2.Nxc5 mate, but 1...Bb6! denies White the mate he seeks.
After 1.Rf5, Black must move his rook from d6 to give the king an escape square. 1...Rdc6? allows 2.Bxd5 mate, but 1...Ra6! (or Rb6) again stops the mate.
Those variations should tell us what to look for: some sort of interference between the black rook and bishop on the b6 square. If we can find an opening move that contains a threat that can be met only by Bb6 or Rb6, we can meet the first with 2.Rf5 (when 3.Nf4 mate will be unstoppable), and the second with 2.Ng6 (followed by 3.Nf8 mate or 3.Nxc5 mate). White's first move, however, must not disrupt any of his existing mating possibilities.
The answer is beautiful and surprising: 1.Kf1! threatening 2.Bd1 and 3.Bg4 mate. Since 1...Bc7 allows 2.Nxc5 mate, Black has only two ways to try to defend: 1...Bb6 (to meet Bd1 with Rg8) which is met by 2.Rf5 Rc6 (to stop Nf4 mate) 3.Bxd5 mate; and 1...Rb6 (to meet Bd1 with Rb1) when 2.Ng6! Bc7 (to stop Nf8 mate) 3.Nxc5 is mate. Finally, note that it has to be 1.Kf1! since 1.Ke1 or Kd2 are met by 1...a4 and 2...Ba5+.