Preheat an oven to 350 F. Lightly grease an 8x8 baking pan and line with parchment paper so that there's a bit of overhang.
Make the crust. Place the cookies in the bowl of a food processor and pulse until the cookies are finely ground. Transfer to a mixing bowl and toss with the brown sugar and melted butter, then press into an even layer in the prepared baking pan. Bake for 10 minutes, then cool slightly.
Lower the oven to 325 F.
Mix the cheesecake filling. In a mixing bowl, beat the cream cheese and sugar together with a hand mixer until smooth. Add the sour cream, eggs, vanilla, and salt and beat until very smooth. Set aside.
Mix the pumpkin pie filling. In a mixing bowl, combine all the pumpkin filling ingredients and whisk together until very smooth and well-mixed. Set aside.
Assemble. Pour all but 1/2 cup of the cheesecake filling into the baked and cooled crust and spread into an even layer. Spread the pumpkin layer over the top. Then, dot the remaining cheesecake over the top and use a knife to swirl the two flavors together.
Bake. Transfer to the oven and bake for 50-55 minutes, until lightly puffed. The center should still jiggle slightly, but be set. Let the pumpkin cheesecake bars cool to room temperature, then refrigerate for at least 4 hours before cutting and serving.