Preheat your oven to 350°F. Line a 9x9-inch baking pan with parchment paper, leaving some overhang for easy removal. Lightly grease the parchment paper.
In a medium bowl, whisk together the flour, baking soda, cinnamon, pumpkin pie spice, and salt. Set aside.
In a large bowl, whisk together the pumpkin puree, granulated sugar, brown sugar, oil, eggs, and vanilla extract until smooth.
Gradually fold the dry ingredients into the wet ingredients, stirring just until combined. Be careful not to overmix.
In a separate bowl, beat the softened cream cheese and sugar together until smooth and creamy. Add the egg and vanilla extract, and continue beating until fully incorporated.
Spread about 2/3 of the pumpkin bread batter into the prepared baking pan, smoothing it out into an even layer.
Carefully spread the cream cheese mixture evenly over the pumpkin batter. It helps to drop spoonfuls of the cheesecake mixture across the surface and then gently smooth it out.
Dollop the remaining pumpkin bread batter on top of the cheesecake layer. Use a butter knife or skewer to gently swirl the pumpkin and cheesecake layers together, creating a marbled effect.
Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs. The cheesecake layer should be set but still soft.
