That's interesting! The first question I had after seing the solution was; So what the heck do I do from here? :D

 I agree that it's hard to see the use of Bh3. The only thing I can think of is that white can't move his g1-rook as long as the white knight is on e1. The problem is that if white moves his e1-knight he loses material to Bg2+. So it might be that Bh3 temporarily locks down whites' kingside pieces. Can it be used somehow?

 I also find it hard for white to do anything constructive with only his queen able to move freely. 

  

Samurai, the whole puzzle made sense to me except the last move:

 

Bh3 was my first instinct. It looks scary, but then I asked, what does it lead to? I don't see an immediate winning continuation.

b5 was my second thought. When you don't see a tactic in an endgame, it's principled to advance your pawns towards promotion.

Be6 is my final idea, planning Ra2 and a seventh-rank attack that threatens White's f-pawn. An eventual Bh3 will be deadly in this line!

I am not so strong at tactics, so maybe I missed something.