Preheat the oven to 325 degrees F (165 degrees C).
Beat cream cheese, sugar, and vanilla extract together in a large bowl with an electric mixer until smooth. Add eggs, one at a time, blending cheesecake layer until well combined after each addition.
Spread 1 cup batter in crust.
Add pumpkin puree, cinnamon, cloves, and nutmeg to remaining batter; stir gently until pumpkin layer is well blended.
Carefully spread on top of cheesecake layer.
Bake in the preheated oven until edges puff and surface is firm except for a small spot in center that jiggles when the pan is gently shaken, 35 to 40 minutes.
Remove from the oven, set on a wire rack; cool to room temperature, 1 to 2 hours.
Refrigerate until set, at least 3 hours or overnight, before slicing.
