Make The Crust: Preheat oven to 350°F/175°C. Wrap the bottom and sides of the cake pan with a double layer of aluminum foil. It’s important to use heavy-duty foil because it comes in wider sheets and does a better job of preventing water from seeping into the pan.
In a medium bowl, combine cracker crumbs, sugar, cinnamon (or pumpkin pie spice) and melted butter and mix until combined. Press mixture into the bottom of the prepared pan to form an even layer. Bake for 10-12 minutes until golden brown. Cool on a wire rack while you prepare the filling.
Reduce oven temperature to 325°F/160°C.
Make The Cheesecake Filling: In a medium bowl, whisk together the pumpkin puree, vanilla, heavy cream, and spices and set aside. Also, set a kettle of water to boil so you can use it for the water bath.
In a mixing bowl of a stand mixer fitted with the paddle attachment or in a large bowl with an electric mixer, beat cream cheese on medium speed until smooth and fluffy, about 1-2 minutes. Add granulated sugar and brown sugar, followed by cornstarch and beat until combined. Scrape down the sides and bottom of the bowl as needed. Add eggs to the mixture, one at a time, making sure each addition is fully incorporated. Then, slowly add the pumpkin puree mixture to the cheesecake mixture and continue to mix on a low speed until everything is combined and the batter is smooth.
Pour batter over the pre-baked crust and spread evenly. Smooth out the top if needed. Place the cheesecake pan into a large roasting pan and pour boiling water into the roasting pan until it reaches about halfway up the side of the cake pan. Bake for 60-70 minutes until the cake is set but the center is still slightly wobbly.
Remove the roasting pan carefully from the oven and let the cheesecake cool in the water bath, then leave it out on a rack to cool completely. While the cake is slightly cool, run a knife around the sides of the pan to release the cake from the pan. Let the cake cool completely. Cover the cake with plastic wrap and refrigerate for at least 4 hours, preferably overnight.
Slice and serve. Add toppings if desired. Cheesecake can be kept in the refrigerator for up to 5 days.