Took me several minutes to eliminate one plausible try, but finally 'got' it. Although there are no branches to the solution, the second move doesn't exactly leap to the eye, which is why, I think, the key move doesn't either. The idea of finding a first move for Black that DOESN'T involve the king does come pretty quickly, though...
Essentially quite easy as you have to give the black king some space to break the stalemate. The idea of creating this space by creating a death trap cave is quite original.