Cream Cheese Mixture: In a stand mixer or with a hand mixer, beat the cream cheese for 2 minutes until creamy.
Add Sugars: Add the granulated and brown sugars, and beat for 1 minute. Scrape down the sides, then beat for another 2 minutes until smooth.
Add Sour Cream: Mix in the sour cream until combined.
Add Eggs: Add the eggs one at a time, mixing well after each addition. Scrape down the bowl as needed.
Add Vanilla: Mix in the vanilla extract.
Prepare Pumpkin Batter: Remove 2 cups of the cheesecake batter and place in a separate bowl. Add the pumpkin puree, pumpkin spice, cinnamon, and nutmeg. Mix on low until just combined.