Preheat your oven to 350°F (175°C). Grease a 9-inch springform pan.
In a large mixing bowl, combine the pumpkin puree, sugar, vegetable oil, eggs, and vanilla extract. Mix until smooth.
In another bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Pour the pumpkin cake batter into the prepared pan and spread it evenly.
In a separate bowl, beat the cream cheese until smooth. Add the sugar, eggs, and vanilla extract, and beat until well combined.
Carefully spread the cheesecake batter over the pumpkin cake layer in the pan.
Bake in the preheated oven for about 60 minutes, or until the cheesecake is set and the edges are lightly browned.
Allow the cake to cool in the pan before removing the springform ring. Refrigerate for at least 4 hours before serving.