Preheat the oven to 325 F. Wrap the outside of a 9-inch springform pan with a double layer of aluminum foil. Mix the gluten free graham cracker crumbs, 1/3 cup sugar, and melted butter until evenly moistened. Press firmly into the bottom and about 1 inch up the sides of the pan. Bake for 10 minutes, then set aside.
In a large bowl, beat the softened cream cheese on medium speed until completely smooth, about 3 minutes. Add 1 cup sugar and beat until combined. Mix in the sour cream, vanilla extract, and gluten free 1-to-1 baking flour.
Add the eggs one at a time, beating on low speed just until each is incorporated. Do not overmix. Gently stir in the heavy cream until the filling is smooth.
Pour the filling over the crust. Place the springform pan inside a large roasting pan. Pour hot water into the roasting pan until it reaches about halfway up the sides of the springform pan. Bake for 1 hour and 15 minutes to 1 hour and 20 minutes until the edges are set but the center still has a slight jiggle.
Turn off the oven and crack the door open. Let the cheesecake cool inside the oven for 1 hour. Remove from the water bath, discard the foil, and refrigerate for at least 6 hours or overnight before removing the springform ring and slicing.