Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan and set aside.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, ground nutmeg, ground cloves, and ground ginger until well combined.
In a large bowl, combine 1 cup granulated sugar, light brown sugar, and vegetable oil. Beat with a mixer on medium speed until smooth.
Add the eggs one at a time to the sugar and oil mixture, beating well after each addition.
Mix in the pumpkin puree and 1 teaspoon vanilla extract until fully incorporated.
Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Pour the pumpkin bread batter evenly into the prepared springform pan and smooth the top with a spatula.
In a separate bowl, beat the softened cream cheese until smooth and creamy.
Add 1/2 cup granulated sugar to the cream cheese and beat until combined.
Add 1 large egg and 1/2 teaspoon vanilla extract to the cream cheese mixture and beat until smooth.
Carefully spoon the cream cheese mixture over the pumpkin bread batter in the pan, spreading it evenly.
Using a knife or skewer, gently swirl the cream cheese layer into the pumpkin bread batter to create a marbled effect.
Bake in the preheated oven for 60 to 70 minutes or until a toothpick inserted near the center comes out with only a few moist crumbs.
Remove the pan from the oven and allow the pumpkin bread cheesecake to cool completely on a wire rack.
Once cooled, refrigerate the cheesecake for at least 4 hours or overnight to set before removing from the springform pan and serving.