Very instructive endgame motive

Basically black can do nothing, it's a zugzwang, a very long one. I just had to move my pawns to the squares where I'd like them to be, and keep moving with the king on black squares.

Amazing! That one White rook paralyzing two of Black's pieces!

That Be4 is a monster, cannot be moved and prevents black from unpinning his bishop.
I guess Black's best chances are to give up g and h pawns to activate the rook

Yeah, he pretty much had to move his king toward the queenside (dim though that prospect may be).

The alternative looked straight out of the pages of Chernev. :)

Very instructive indeed, well played.