Well, it looks like White's main obstacle is that he is about to lose a piece, upsetting his material advantage. If the d3-Knight is defended, Qg7+ picks up the Rook. I initially thought 1.Nf4 may be a good try, as 1...Qg7+ 2.Rg6 hxg6 3.Ne6+ would pick up the Queen, but then 1...Qd2+ complicates matters again.
However, this does lead us to some interesting lines. 1.Nf4 Qd2+ 2.Kg3 Qxc2 gives us a tempo, as White has no checks. In fact, it may even be possible to try 3.Kg4, allowing the King to participate in a possible attack. This could get complicated, and I don't have time right now to look at it in depth.
This is the first study that I composed, and it had a larger impact than I expected. It has been discussed intensively in some chess forums and in the near future it will be part of a chess studies book... I'll attach references later. Enjoy! [Hint] Computers may (badly) misevaluate this position long time into the solution
and I enjoy mocking the chess engines.
White to move and win.