Preheat your oven to 325°F and wrap the outside of a 9-inch springform pan with two layers of foil. In a bowl, combine the gluten free graham cracker crumbs, melted butter, sugar, and cinnamon until evenly moistened.
Press the mixture firmly and evenly into the bottom of the pan. Bake for 10 minutes, then set aside to cool. In a large bowl, beat the cream cheese, granulated sugar, and brown sugar together on medium speed until completely smooth and fluffy, about 4 minutes. Scrape down the sides and bottom of the bowl thoroughly.
Add the cornstarch, cinnamon, and vanilla extract and beat on low until well combined. Add the eggs one at a time, mixing on low after each just until incorporated. Fold in the sour cream gently by hand with a spatula.
Pour the filling over the cooled crust and smooth the top. Place the pan in a large roasting pan and add hot water to the roasting pan until it reaches halfway up the sides of the springform pan. Bake for 55 to 60 minutes, until the cheesecake edges are firm and the center still jiggles slightly.
Turn off the oven, crack the door open a few inches, and let the cheesecake cool inside for 1 hour. Remove from the water bath, remove the foil, and refrigerate for at least 6 hours or overnight until fully set.
When ready to serve, brush the top of the chilled cheesecake with the melted butter. In a small bowl, mix the sugar and cinnamon together, then sprinkle it evenly over the buttered surface so it sticks in a generous layer.
Gently warm the dulce de leche in the microwave for 15 to 20 seconds until pourable, then drizzle it over the top of the cheesecake. Slice and serve immediately.