Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan and line the bottom with parchment paper.
In a medium bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, nutmeg, cloves, and ginger until well combined.
In a large bowl, beat together 1 cup granulated sugar, brown sugar, pumpkin puree, vegetable oil, 2 eggs, and 1 teaspoon vanilla extract until smooth and well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Set the pumpkin bread batter aside.
In a separate large bowl, beat the softened cream cheese with 2/3 cup granulated sugar until smooth and creamy.
Add 2 eggs one at a time to the cream cheese mixture, beating well after each addition.
Mix in sour cream and 1 teaspoon vanilla extract until fully incorporated and smooth.
Pour half of the pumpkin bread batter into the prepared springform pan and spread evenly.
Carefully pour the cheesecake filling over the pumpkin bread layer, spreading gently to cover evenly.
Top with the remaining pumpkin bread batter and spread gently to cover the cheesecake layer.
Using a knife or skewer, gently swirl the top layers together to create a marbled effect.
Bake in the preheated oven for 60 to 70 minutes, or until the cheesecake center is set but still slightly jiggly.
Remove the pan from the oven and allow the cheesecake to cool to room temperature.
Once cooled, refrigerate the pumpkin bread cheesecake for at least 4 hours or overnight before removing from the springform pan and serving.