White needs to put his bishop on f6 in order to create winning chances, so a good way to start is by playing f3, planning Be1-h4-f6, followed by Qf2, with two ideas: either Qh4, Rg5-h5 (possibly with Rdg1 first if necessary), or Rg3-h3, then Rxh7, with mate in either case.
The first question is whether black can defend against this by moving his king to the queenside, and playing h5 at the right moment. But a more important question (as the former is a best case scenario in which white cannot lose) is whether black's counterattack on the queenside with b6 and a5 or c5 may end with white getting mated (as white's plan is slow, whereas black's counterattack is quick, though mate is not obvious).
But in any case, with the white pieces, you must realise that lines will be opened on the queenside, so black can also play for a win. The only reason why white may claim an advantage in this position is because his bishop may potentially have a future over black's, but this isn't necessarily true if black can find a good square for his bishop if and when he plays c5 and d4.
So f3 and manoeuvring the bishop to f6 is white's only way to win; black has the option of defending or counterattacking. Conversely, white can attempt to establish a grip on the dark squares by playing Be3 and c3, and try to hold the position to a draw, but this seems unlikely as black will be able to crash through.
Long story short: white's plan as described is practically forced, but whether he will win or not is a different story.
