Combine graham cracker crumbs, butter, and ⅓ cup sugar in a bowl; press into the bottom and a little bit up sides of a 9-inch square baking pan. Refrigerate until ready to use.

Preheat the oven to 325 degrees F (165 degrees C).

Beat cream cheese, ½ cup sugar, and vanilla extract together in a bowl with an electric mixer until smooth. Beat in eggs, one at a time. Spread 1 cup cream cheese batter onto graham cracker crust.

Add pumpkin purée, cinnamon, cloves, and nutmeg to remaining cream cheese batter; stir gently until well combined. Carefully spread pumpkin batter over cream cheese batter.

Bake in the preheated oven until the center is set, 35 to 40 minutes. Cool at room temperature for 20 to 30 minutes, then place in the refrigerator until firm, about 3 hours. Cut into 16 squares; top with whipped topping.