I came across this wonderful thinking exercise over at Dennis Monokroussos' blog, The Chess Mind and have reproduced it here with permission.

It's not your typical puzzle, and by that I mean it's not a position in which there's a key winning move or correct answer.  Instead, this position is the equivalent of chessic trench warfare!  The battle will be a difficult, protracted contest between two evenly matched enemies along a clearly formed demarcation line.   With strengths and weaknesses on both sides, it's possible that the struggle will all be for naught.  In this challenging thinking exercise, there is only one goal:

Can you find a way for white to win?

Thompson,

In your game, if black doesn't go with 4...Ke4 but instead moves 4...Bc7 then you've been stopped dead in your tracks because now your bishop can't move to c8 and occupy the important diagonal. 

I think the key to this position is to delay the advance of the d-pawn by doing something like this:

1.g4 Bd6 Bd7 Bb8 d6 Bxd6 Kd5 Bb8 Bf5 and whatever black plays, white would seem to have a decided advantage...

Or

1.g4 Bd6 Bd7 Ke7 Bf5 Kf6 Bc8 Bb8 d6 Bxd6 and again I think white has a strong hand.