Preheat the oven to 325°F (165°C).

Prepare the Cheesecake Layer: In a large bowl, beat the softened cream cheese, white sugar, and vanilla extract until smooth. Add the eggs one at a time, blending well after each addition.

Pour half of the cheesecake batter into the prepared graham cracker crust, spreading it evenly.

Prepare the Pumpkin Layer: In the remaining cheesecake batter, add the pumpkin puree, ground cinnamon, ground cloves, and ground nutmeg. Stir gently until well blended.

Carefully spread the pumpkin mixture over the plain cheesecake layer in the crust.

Bake in the preheated oven for 35 to 40 minutes, or until the edges are puffed and the surface is firm except for a small spot in the center that jiggles when the pan is gently shaken.

Remove from the oven and set on a wire rack to cool to room temperature, about 1 to 2 hours.

Refrigerate for at least 3 hours before serving, preferably overnight.