This is quite complicated, but I think 1.N4f5 is the right move- it breaks the protection of the black knight at d3, and it threatens both NxQ and Qg7#. I think black has two options for his first move- either an immediate Qf6 or first Bxf2+. Let's look at the first option:

1.N4f5 Qf6 2.Qd3

I looked a long time at the various options after 2.Qxf6 for white, but they are just too complicated and unclear to me- I think white gains an edge in several of them, but not as clear cut to me as just taking the knight at d3. Continuing:

2.......Rbd8

Attacking the weakness in white's structure- the knight pair protecting each other:

3.Qg3

Breaking the pin and keeping the knight under guard:

3......Bb8 4.Ne4!

Untangling the position and consolidating:

4.......Qb2 5.Qf3 Qe5 6.Nge3 Bf5 7.Qf5 and white has won a piece for a pawn. There may be better moves for both players, but I more confident I have found the best defense for black in this line than I am confident about the line for white being best.

The alternative at move 1 for black might be a better line overall for black, but I am unsure- this line is mostly speculation on my part, and not necessarily all that deep an analysis:

1.N4f5 Bf2+ 2.Kh2! (not 2.Kg2?! Nf4+) 3.Qd3 Bc5 4.Qg3 Bd6 5.Nd6 Qb2+ 6.Kh1 Rbd8 7.Ra2 Qd4 8.Rd1 Qb4 9.Rf2 and maybe this is better for black over the first line, but I am less sure of whites early moves here- maybe 3.Qxf6 is better in this line- it certainly looks a bit better for white's king overall. Just hideously complicated.