Grease a 9-inch springform pan with butter or shortening. Set aside.
Start by making the crust. Place the graham crackers in a food processor and blend at high speed until the graham crackers are finely chopped.
Slowly pour the melted butter into the food processor while running it at low speed until the crumbs start to pull away from the sides.
Add the crumbs into the greased pan, press them evenly and firmly into the base. Set in the freezer for at least 20 minutes.
While the crust is freezing, prepare the cheesecake filling. Add the cream cheese, sugar, and brown sugar to a large bowl. Beat at medium speed with an electric hand mixer until the ingredients are well mixed and smooth. Make sure there are no lumps.
Add the pumpkin puree and pumpkin pie spice, and continue beating at medium speed until the mixture is smooth.
Fold the thawed whipped topping into the cream cheese mixture until well combined.
Spread the cheesecake filling over the frozen crust, cover and refrigerate for at least 4 hours or until the cheesecake has set completely.
Top with whipped cream and ground cinnamon. Serve chilled.