Preheat the oven. Preheat to 350°F (175°C). Lightly grease a 9-inch (23 cm) springform pan.
Make the crust. Combine the graham cracker crumbs and granulated sugar in a bowl. Stir in the melted butter until the crumbs are evenly moistened. Press gently into the bottom and partway up the sides of the pan.
Prebake the crust. Bake for 10 minutes. Set aside while preparing the filling. Keep the oven at 350°F (175°C).
Mix the cheese and sugars. Beat the cottage cheese with the granulated sugar. Add the light brown sugar and mix until evenly combined, scraping down the bowl as needed. Small cottage cheese curds may remain.
Add the pumpkin and sour cream. Mix in the pumpkin purée and sour cream until incorporated, then add the vanilla extract.
Add the eggs and cornstarch. Add the eggs one at a time, mixing on low speed just until incorporated after each addition. Add the cornstarch and mix briefly until combined. Avoid overmixing.
Fill the pan. Pour the filling over the prebaked crust and gently smooth the top.
Prepare the water bath. Wrap the outside of the springform pan with several layers of heavy-duty foil, covering the bottom and sides. Place it inside a large roasting pan. Set the roasting pan in the oven and carefully add hot water to reach about halfway up the sides of the springform pan.
Bake. Bake for about 1 hour, until the edges are set and the center still has a slight wobble. If the center looks liquid, continue baking, checking every few minutes.
Cool. Carefully remove the cheesecake from the water bath, take off the foil, and place the pan on a wire rack. Allow to cool, then refrigerate within 2 hours of removing it from the oven.
Chill. Refrigerate for at least 4 hours, preferably overnight, until thoroughly chilled and firm.
Decorate and serve. Gently loosen the edges and remove the springform ring. Dust lightly with cinnamon and decorate with whipped cream and small cookies, if desired. Slice and serve chilled.
