Set out the cream cheese well in advance. Cream cheese should be at room temperature before use to avoid lumps in your cheesecake.
Preheat the oven to 425 degrees.
Prepare the pumpkin pie batter.
In a medium mixing bowl, whisk together 1 cup pumpkin, 1/2 can (approximately 1/2 cup plus 2 Tbsp.) sweetened condensed milk, 1 egg, 1/2 teaspoons ground cinnamon, 1/4 teaspoons ground nutmeg, 1/4 teaspoons ground ginger and 1/4 teaspoons salt until smooth. Pour pumpkin pie batter in pie crust.
Prepare the plain cheesecake batter.
In a second mixing bowl, combine both packages of room temperature cream cheese, 1/2 cup white sugar and 1/2 teaspoons vanilla extract using a hand mixer. Blend until the mixture is smooth. Add 2 eggs, one at a time, blending thoroughly after each addition. Remove 1 cup of the plain cheesecake batter and spread gently on top of the pumpkin pie batter.
Prepare the pumpkin cheesecake batter.
Add 1/2 cup of pumpkin puree, 1/2 teaspoons ground cinnamon, 1/8 teaspoons ground cloves, and 1/8 teaspoons ground nutmeg to the remaining plain cheesecake batter. Stir gently until well blended. Pour pumpkin cheesecake batter gently over cheesecake batter.
Bake for 10 minutes, then lower the oven to 350 and continue to bake for 20 minutes. Lower the oven to 300 and continue to bake for 15 to 20 minutes, making sure the outer edge doesn’t brown too much. The center should still be soft with the edges firmer. The center will firm up as it cools off. Allow the cheesecake to cool completely, and then place it in the refrigerator for at least 3 hours before serving.