i'd respond Kc3.
Can W win from here?

I have made changes - sorry for the confusion.
1.Kc3 Black responds by moving Be7-f8 What should White respond?

How about Nd2 followed by Ne4. This leaves the black bishop completely stuck. Not sure how it would continue though

Hint: press Move List for all the variations!
White has the superior Kt and the e7 pawn but that pawn is blockaded plus Black just moves his bishop e7-f8 or the K to c5 if White tries to move his Kt to d4-c6.
How should White respond? What is White's plan?