Step 1: Preheat your oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving an overhang on the long sides for easy removal.
Step 2: Make the Crust: In a medium bowl, combine graham cracker crumbs, ¼ cup granulated sugar, and melted butter. Mix until evenly moistened. Press the mixture firmly into the bottom of the prepared baking pan.
Step 3: Bake the crust for 8-10 minutes, or until lightly golden. Remove from oven and let cool slightly while preparing the fillings.
Step 4: Prepare the Pumpkin Layer: In a large bowl, using an electric mixer, beat 8 ounces softened cream cheese until smooth. Add pumpkin puree, ½ cup granulated sugar, brown sugar, egg, pumpkin pie spice, and ½ teaspoon vanilla extract. Beat on low speed until just combined and smooth, scraping down the sides of the bowl as needed. Do not overmix.
Step 5: Pour the pumpkin cheesecake mixture evenly over the cooled graham cracker crust. Spread gently with an offset spatula.
Step 6: Prepare the Cheesecake Swirl: In a separate small bowl, beat 4 ounces softened cream cheese with ¼ cup granulated sugar, egg yolk, and ½ teaspoon vanilla extract until smooth.
Step 7: Dollop spoonfuls of the plain cheesecake swirl mixture over the pumpkin layer. Using a thin knife or skewer, gently swirl through the two layers to create a marbled pattern.
Step 8: Bake for 35-40 minutes, or until the edges are set and the center has a slight jiggle. Do not overbake. Remove from oven.
Step 9: Let the bars cool completely on a wire rack at room temperature. Once cooled, refrigerate for at least 2 hours, or preferably overnight, before slicing and serving. For clean slices, wipe your knife with hot water between cuts.