Preheat oven to 350°F / 177°C.
Prepare a 9x13 baking dish by spraying it lightly with nonstick cooking spray and lining it with parchment paper (this will make the bars really easy to remove).
In a medium bowl, whisk together graham cracker crumbs and 3 Tablespoons of granulated sugar. Pour melted butter over top and stir until evenly combined. Pour the crumbs out into the prepared pan and press the crumbs firmly down until solid and even. (Note: I like to use the back of a measuring cup to help press the crumbs down in an even layer.)
In a stand mixer using the whisk attachment, or using a hand mixer, beat the cream cheese until soft and smooth. Add in 3/4 cups of granulated sugar, all of the brown sugar, and the flour and beat until light and fluffy, 2 to 3 minutes.
Add in pumpkin puree, pumpkin pie spice, and vanilla. Mix on low speed until even.
Add in the eggs one at a time, mixing on medium speed just until each egg is incorporated.
Add the heavy cream and mix on low just until the entire mixture is smooth and even.
Pour filling over the crust. Tap the pan lightly on the counter to release any air bubbles.
Bake until the center is just set, and looks shiny and still slightly wobbly, 35 to 40 minutes.
Let the cheesecake bars cool completely at room temperature. Refrigerate, covered, until ready to serve, up to 3 days. Slice and top with whipped cream just before serving.