Combine graham cracker crumbs, butter, and sugar for crust. Press onto the bottom and a little bit up the sides of a 9-inch square baking pan. Place in the refrigerator until ready to use.
Preheat the oven to 325 degrees F (165 degrees C).
Combine cream cheese, sugar, and vanilla extract for filling in a mixing bowl; beat with an electric mixer until smooth. Beat in eggs, one at a time. Remove 1 cup of batter and spread it onto bottom of the graham cracker crust.
Add pumpkin, cinnamon, cloves, and nutmeg to remaining cream cheese mixture and stir gently until well blended. Carefully spread the pumpkin mixture over the cream cheese mixture you already placed on the crust.
Bake in the preheated oven until the center is set, 35 to 40 minutes. Remove from the oven and allow to cool, 20 to 30 minutes. Place in the refrigerator until firm, about 3 hours. Cut into 16 squares and top with whipped topping.