I made these cookies for a lunch meeting last week. NFSC with fondant, then EI.

Another time I will roll the fondant circles a little more after cutting them, so they will cover the whole cookie. Used the same cutter for the cookie and the fondant, but obviously the cookie spread while baking.

Are you putting them in the freezer before baking? I know some people do that to help from expanding like that. Sorry I can't help more.