I'm guessing Qa3 because if the bishop leaves its post pawn comes with double check. This might be utterly wrong thanks for posting the puzzle.

I have looked at this for quite a while and feel like I have to be missing something better, but have no idea what it is. The first move is pretty obvious- 1.Qc3 pinning the knight, and most of the moves in this line below seem obvious to me, too, and do lead to what should be a winning Queens with pawns ending for white where the white king is quite safe from checks with careful play.

1.Qc3 Rxb5 2.Rc5 Qd1+ 3.Kg2 Rxc5 4.Rxc5 Bxc5 5.Qxe5+ Kxf7 6.Qxc5 should win. Black cannot capture with the bishop at move 3 because the of the capture at e5 comes with check and the pawn on f7 still protected in that case, which leads to a really quicker ending.