Preheat the oven to 350°F (175°C).
Grease a 9x13-inch baking pan and set aside.
Beat the cream cheese and sugar in a medium bowl until smooth.
Add the eggs one at a time, then vanilla, mixing until combined. Set aside.
Whisk the pumpkin puree, brown sugar, oil, and eggs in a separate bowl until smooth.
Mix the flour, baking powder, baking soda, salt, and spices in another bowl.
Gradually combine wet and dry ingredients.
Transfer 1 1/2 cups of the pumpkin cake batter into an even layer in the prepared pan.
Alternate spoonfuls of cheesecake and remaining pumpkin batter on top.
Swirl slightly with a knife.
Bake for 50 to 60 minutes, or until a toothpick inserted in the center comes out mostly clean (a few crumbs are okay).
Cool completely at room temperature, then refrigerate for at least 3 hours before serving.