1. For the crust: Preheat the oven to 300°F.
2. Line a 9 by 13-inch baking dish with parchment paper, leaving about 1 inch of paper hanging over the sides.
3. In a medium bowl, combine the graham cracker crumbs with the melted butter. With your fingers, press the crust into the bottom of the prepared pan. Set aside while making the filling.
4. For the filling: Using a hand mixer or a stand mixer fitted with the paddle attachment, beat the cream cheese and sugar on medium speed until light and fluffy. Beat in the eggs, one at a time, just until blended. Spoon half of the mixture over the crust and spread evenly.
5. Add the pumpkin puree and pumpkin pie spice to the remaining mixture. Beat until smooth. Carefully spoon over the mixture in the pan.
6. Bake for 50 minutes, or until just set. Turn off the oven and leave the door ajar, allowing the cheesecake to slowly cool down for about 1 hour or so. Refrigerate for at least 3 hours. Cut into bars, top with whipped topping, and serve.