Prep & Preheat: Preheat oven to 325°F (165°C). Line an 8x8-inch or 9x9-inch square baking pan with parchment paper, leaving an overhang on the sides for easy lifting.
Press the Crust: In a medium bowl, combine graham cracker crumbs, sugar, cinnamon, and melted butter until sandy. Press firmly into an even, compact layer on the bottom of the prepared pan using the flat bottom of a measuring cup. Pre-bake at 325°F for 8 minutes, then remove and let cool slightly.
Beat Cream Cheese Base: In a large bowl using an electric hand mixer on medium-low speed, beat softened cream cheese until smooth and creamy (about 2 minutes). Add granulated sugar and brown sugar, beating until completely combined and lump-free. Add eggs one at a time, beating just until incorporated, then stir in vanilla extract and flour.
Divide & Spice Pumpkin Batter: Set aside 1/2 cup of the plain vanilla cheesecake batter. To the remaining batter in the bowl, add pumpkin purée and pumpkin pie spice. Whisk gently until fully blended and silky orange.
Layer & Swirl: Pour the spiced pumpkin cheesecake mixture over the pre-baked crust. Drop dollops of the reserved plain vanilla batter on top. Drag a butter knife or skewer through the dollops in gentle figure-eight motions to create an elegant marble swirl pattern.
Bake, Cool & Chill: Bake at 325°F (165°C) for 32 to 36 minutes until the edges are set and slightly puffed, but the center still has a gentle slight wobble. Turn off oven, crack the door slightly, and let rest for 20 minutes. Cool completely to room temperature, then refrigerate for at least 3 hours (or overnight) before slicing into 16 clean bars with a warm knife.