In a separate, large mixing bowl combine the cream cheese and brown sugar together and beat of medium speed for 2 to 3 minutes using a handheld mixer. Scrape down the sides of the bowl, add in the heavy cream and vanilla extract and continue to mix the ingredients together until thoroughly combined. Filling should be smooth without any lumps. Pour the cream cheese filling on top of the graham cracker crust and smooth it out with an off set spatula to create a smooth, even layer. Cover with plastic wrap and store in the refrigerator over night to firm up and set.