Preheat the oven to 350°F (175°C). Grease and flour a 9-inch springform pan.
In a medium bowl, whisk together the flour, baking soda, salt, cinnamon, nutmeg, cloves, and ginger until well combined.
In a large bowl, beat together the granulated sugar, brown sugar, pumpkin puree, vegetable oil, eggs, and vanilla extract until smooth and well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
Pour the pumpkin bread batter into the prepared springform pan and spread evenly.
In a separate large bowl, beat the softened cream cheese until smooth and creamy using an electric mixer on medium speed.
Add the granulated sugar and beat until combined and smooth.
Add the egg, pumpkin puree, vanilla extract, cinnamon, and nutmeg to the cream cheese mixture and beat until smooth and fully incorporated.
Carefully spoon the cheesecake mixture over the pumpkin bread batter in the pan, spreading it evenly.
Bake in the preheated oven for 60 to 70 minutes, or until the cheesecake is set and the edges are lightly golden. The center should still have a slight jiggle.
Turn off the oven and leave the cheesecake inside with the door slightly open for 1 hour to cool gradually.
Remove the cheesecake from the oven and allow it to cool completely at room temperature.
Refrigerate the cheesecake for at least 4 hours or overnight before removing the springform pan and serving.
Slice and serve chilled.