Preheat oven to 325°F. Line a 9x13-inch pan with a parchment paper sling for easier removal and cutting.
Pulse graham crackers in a large food processor until broken up into fine crumbs. Add sugar and melted butter, pulsing until the graham cracker crumbs are evenly moistened.
Press crust mixture into the prepared pan. Bake for 10-12 minutes to set the crust, then remove it from the oven to cool slightly before adding the cheesecake filling.
Beat cream cheese, granulated sugar, brown sugar, and vanilla with an electric mixer until creamy and smooth. Stop to scrape the bottom and sides of the bowl with a rubber spatula.
Add sour cream and eggs, one at a time. Mix on low speed after adding each egg, just until everything is evenly combined and the cheesecake batter is smooth.
In a separate bowl, combine 1 ½ cups of the plain cheesecake batter with the pumpkin puree, cinnamon, ginger, nutmeg, allspice, and cloves.
Use cookie scoops to dollop large spoonfuls of the different batters onto the graham cracker crust, alternating between the two. Gently swirl the batters together with a knife to create a marble effect, being careful not to scrape up the crust underneath.
Bake for 35 to 45 minutes until set around the edges and only every so slightly jiggly in the center. Remove from the oven and let the bars cool at room temperature.
Transfer the cooled pumpkin cheesecake bars to the fridge and chill for 6 hours or overnight until completely cold. Once chilled, carefully remove the slab of cheesecake bars from the pan with the parchment paper sling and cut into 24 squares using a sharp knife to serve.