Prep the pan: Heat oven to 325°F (163°C). Line a 9x13-inch baking pan with parchment, leaving overhang on the long sides for easy lifting. Lightly grease the parchment.
Make the crust: In a bowl, combine crumbs, sugar, cinnamon, salt, and melted butter.
Stir until the mixture looks like wet sand. Press firmly and evenly into the lined pan, packing the corners well.
Par-bake crust: Bake the crust for 8–10 minutes until fragrant and set. Remove and let cool slightly while you make the filling.
Keep the oven at 325°F.
Beat the cream cheese: In a large bowl, beat cream cheese with a hand mixer (or stand mixer) on medium speed for 2 minutes until smooth and fluffy. Scrape the bowl.
Add sugars and dry ingredients: Beat in granulated sugar, brown sugar, cornstarch, and salt until smooth, about 1 minute. Scrape the bowl again.
Add eggs and flavor: Beat in eggs one at a time on low speed just until combined.
Mix in vanilla and sour cream on low until silky. Do not overbeat.
Make the pumpkin portion: Transfer about 1 1/2 cups of the cheesecake batter to a separate bowl. Whisk in pumpkin puree, cinnamon, ginger, nutmeg, cloves (if using), and maple syrup or sugar until smooth.
Assemble the layers: Pour the remaining plain cheesecake batter over the crust and smooth.
Spoon the pumpkin batter over the top in large dollops.
Create the swirl: Use a butter knife or skewer to gently swirl the pumpkin mixture into the plain batter. Aim for a few broad figure-eights—avoid overmixing.
Bake: Bake for 35–42 minutes, until the edges are set and the center wobbles slightly when you nudge the pan. The surface should look mostly set without browning too much.
Cool gradually: Turn off the oven, crack the door, and let the bars rest inside for 10 minutes.
Move to a wire rack and cool to room temperature, about 1 hour.
Chill: Refrigerate for at least 4 hours, preferably overnight, until firm enough to slice cleanly.
Slice and serve: Lift out using the parchment overhang. Use a sharp knife, wiping between cuts for neat edges. Serve plain or with a light drizzle of caramel or a dollop of whipped cream.