Preheat and Prepare the Pan: Preheat your oven to 325°F (163°C). Line a 9x9 inch baking pan with parchment paper, leaving some overhang on the sides for easy removal.
Make the Crust: In a medium bowl, mix the graham cracker crumbs, sugar, and melted butter until well combined. Press the mixture evenly into the bottom of the prepared pan. Bake for 10 minutes, then let it cool slightly while you prepare the filling.
Prepare the Cheesecake Filling: In a large bowl, beat the cream cheese and sugar together until smooth. Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract until fully incorporated.
Prepare the Pumpkin Swirl: In another bowl, combine the pumpkin puree, sugar, egg yolk, cinnamon, nutmeg, and ginger. Mix until smooth and well combined.
Assemble the Bars: Pour the cheesecake filling over the cooled crust, spreading it evenly. Drop spoonfuls of the pumpkin mixture onto the cheesecake layer. Use a knife or skewer to gently swirl the pumpkin mixture into the cheesecake.
Bake: Bake for 45 minutes, or until the center is set and only slightly jiggles when the pan is gently shaken. Cool the bars in the pan on a wire rack, then refrigerate for at least 4 hours, preferably overnight, before cutting into squares.