In a mixing bowl, combine the graham cracker crumbs, melted butter, and 1/3 cup white sugar. Mix until the crumbs are evenly moistened. Press the mixture firmly into the bottom and slightly up the sides of a 9-inch square baking pan to form an even crust. Refrigerate the crust while you prepare the filling.

Preheat your oven to 325°F (165°C). In a separate bowl, beat the cream cheese, 1/2 cup white sugar, and vanilla extract together with an electric mixer on medium speed until smooth and creamy. Add the eggs one at a time, mixing well after each addition, until fully incorporated.

Spread 1 cup of the cream cheese batter (from Step 2) evenly over the prepared graham cracker crust (from Step 1). To the remaining cream cheese batter, add the pumpkin purée, ground cinnamon, ground cloves, and ground nutmeg. Stir gently until the mixture is well combined. Carefully spread the pumpkin cheesecake batter over the plain cream cheese layer in the pan.

Bake in the preheated oven for 35 to 40 minutes, or until the center is set. Remove from the oven and let cool at room temperature for 20 to 30 minutes, then transfer to the refrigerator and chill until firm, about 3 hours. I find letting them fully chill makes the bars much easier to cut cleanly.

Once the cheesecake bars are fully chilled, cut them into 16 squares. Top each square with a dollop of whipped topping just before serving for a creamy finish.