Preheat your oven to 325°F (163°C).
In a large mixing bowl, beat together the cream cheese, granulated sugar, and vanilla extract until smooth and creamy. Add in the eggs one at a time, blending well after each addition.
Measure out 1 1/3 cups of the cheesecake batter and spread it evenly over the base of the graham cracker crust, setting it aside for layering.
To the remaining batter, add the pumpkin puree and pumpkin spice, stirring gently until fully incorporated. Carefully layer this spiced pumpkin mixture over the plain cheesecake layer, using a spatula to spread it evenly.
Place the cheesecake in the preheated oven and bake for 35-40 minutes, or until the center is just slightly set. Allow the cheesecake to cool at room temperature for about 1 hour.
Once cooled, refrigerate for at least 3 hours, or overnight, to allow it to set fully. Serve chilled with a dollop of whipped cream if desired.