Pour the cream cheese filling over the cooled crust and use an offset spatula to smooth the top.
Dollop the pumpkin pie filling over the top in 14 or 15 dollops. Use the tip of a table knife to swirl the pumpkin into the cream cheese batter, being careful not to cut into the crust. Bang the bottom of the pan on the counter a few times to help get rid of any air bubbles.
Bake the cheesecake until the center registers 150°F (65°C) on an instant-read thermometer and the outside edges are puffed and set but the center is still jiggly, 40 to 45 minutes. Turn off the heat, open the oven door just a crack, and let the cheesecake rest and cool in the warm oven for 30 minutes.
Transfer the pan to a wire rack and let cool. Once the cheesecake is completely cool, place a piece of parchment over the top of the pan (this helps keep condensation off the top of the cheesecake) and transfer it to the refrigerator. Let chill for at least 4 hours or preferably overnight.
Slice into bars and serve. The bars can be served cold or at room temperature but keep best in the refrigerator for up to 2 days.