Why would you want to put parchment paper under your fondant? In theory, that would make it move around while it's cutting and you want the fondant to stick to the mat. All you really need to do is lightly grease the mat and put your fondant on it.
I'm up to my elbows in powdered sugar....LIFE IS SWEET!!!!
I just figured that I would put shortening on the mat to stick the parchment paper on then put shortening on the parchment paper and put the fondant on. I figured it would be a lot easier to take the figures off.