Step 1: Preheat your oven to 325°F (165°C) and line an 8×8 inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
Step 2: In a medium bowl, combine graham cracker crumbs, 1/4 cup sugar, and melted butter. Press the mixture firmly into the bottom of the prepared pan and bake for 10 minutes. Let it cool while you prepare the filling.
Step 3: In a large bowl, beat the softened cream cheese and 1/2 cup sugar until smooth and creamy. Add the eggs one at a time, followed by the vanilla extract, beating on low speed until just combined.
Step 4: Remove 1 cup of the plain cheesecake batter and set it aside. To the remaining batter in the bowl, add the pumpkin puree, cinnamon, ginger, cloves, and nutmeg. Whisk until the pumpkin mixture is smooth and evenly colored.
Step 5: Spread the reserved plain cheesecake batter over the cooled crust. Carefully spoon the pumpkin batter over the plain layer and smooth the top. Bake for 40-45 minutes or until the edges are set and the center is slightly jiggly.
Step 6: Allow the bars to cool to room temperature in the pan, then refrigerate for at least 4 hours, or preferably overnight, before slicing into squares.