Adjust an oven rack to the middle of the oven. Preheat the oven to 325 degrees. Line a 9 by 13 inch pan with a parchment sling.
Whisk together the graham cracker crumbs, granulated sugar, cinnamon, and ginger in a medium bowl. Add the melted butter and mix with a spatula until evenly incorporated.
Press the mixture into the bottom of the prepared pan and bake for 10 minutes. Remove the pan from the oven and let cool. After the pan has cooled, wrap the outsides of the pan with 2 layers of aluminum foil, with the shiny side facing out (this helps keep the sides of the cheesecake from browning).
For the Pumpkin Pie Filling
In a medium bowl, combine the pumpkin, brown sugar, egg, maple syrup, cinnamon, ginger, nutmeg, and salt, and mix until completely combined.
For the Cream Cheese Filling
In a bowl of a stand mixer fitted with a paddle, beat the cream cheese on medium speed until light and completely smooth, 4 to 5 minutes. Scrape down the sides of the bowl often, making sure all the cream cheese has incorporated and is silky smooth. Add the granulated sugar and beat on medium speed until completely incorporated, stopping to scrape down the bowl as needed, 2 to 3 minutes. Add the vanilla and salt, and beat on medium speed for 2 to 3 minutes. Add the eggs one at a time, beating on low speed after each addition until just combined. Using a spatula, give the filling a couple of turns to make sure it is fully mixed.
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 to 15 dollops. Use the tip of a butter 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 of the cheesecake registers 150 degrees, 30 to 35 minutes. The outside 2 to 3 inches of the cheesecake will be puffed and fairly firm and set, but the center will be jiggly at this point. Turn off the heat , and open the oven door just a crack, and let the cheesecake rest 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 overnight. Slice the bars and serve. The bars can be served cold or at room temperature but keep best in the refrigerator for up to 2 days.