For the crust:
Preheat oven to 350 degrees F. Spray the bottom of an 8X8 inch pan with cooking spray or a little bit of oil and cover with parchment paper so that it hangs over the edges. You'll be able to lift it out easier later.
Add cookies to the bowl of a food processor and pulse a few times until completely broken up. Add the melted butter and pulse just 2-3 more times. Press the crust into the pan, completely covering the bottom as evenly as possible.
Bake the crust for 10 minutes. Transfer pan to wire rack to cool completely.
For the filling:
Reduce oven temperature to 325 degrees F.
With an electric mixer on medium speed, beat cream cheese* and sugar until fluffy and smooth. Add flour, salt, and vanilla; beat until combined. Add eggs, 1 at a time, beating after each addition until just combined. Set aside.
In another bowl, use a wooden spoon to stir together pumpkin puree, pumpkin pie spice, cinnamon, and nutmeg. Add 2/3 cups of the cream cheese mixture to the pumpkin mixture and stir together until mixed together.
Assemble the cheesecake by spreading 1 cup of the cream cheese mixture into a thin layer on top of the baked crust. Drop 1 tablespoon dollops of the pumpkin mixture and the cream cheese mixture in the pan, alternating the two to create a checkerboard pattern. With a butter knife or toothpick, swirl the pumpkin filling and the cream cheese filling to create a marbling pattern. Don't worry if it doesn't look perfect! You may have a little pumpkin mixture leftover
Bake for 45-50 minutes. Turn off the oven and let the pan sit in the oven to bring their temperature down slowly. After about 10 minutes, remove from oven and let cool completely.
Refrigerate until chilled, 2-3 hours. Lift the pumpkin cheesecake bars out of the pan, cut into bars and serve.