Preheat oven to 350°F. Spray a 9-inch springform pan with cooking spray and line the bottom and sides with parchment paper. Set it aside.
Mix the brownie mix with the ingredients listed on the box in a medium or large mixing bowl. Pour the brownie batter into the prepared springform pan, and bake it for 15 minutes. You don’t want the brownie layer to be fully baked. Lower the oven temperature to 325°F.
While the brownie bottom is baking, use an electric mixer to mix the cream cheese, sugar, brown sugar, flour, and pumpkin pie spice in a large bowl until smooth. Add the pumpkin puree and vanilla extract and continue mixing until combined. Add the eggs, one at a time, and mix until the eggs are just incorporated. Be careful not to overmix the cheesecake batter.
Carefully spoon the cheesecake batter over the brownie layer, then bake for 40 minutes or until the cheesecake is set on the edges but slightly jiggly in the middle. Turn the oven off, but leave the cheesecake in the oven with the door closed for 1 hour.
After an hour, take the cheesecake out of the oven and let it cool to room temperature on the counter. Once it has cooled, place the cheesecake in the refrigerator for at least 4 hours or until it is completely set.
Before serving, remove the ring of the springform pan and carefully peel off the parchment paper. Transfer the cheesecake to a cake stand or platter, garnish with whipped cream and melted chocolate, if desired, and serve chilled.