Preheat oven to 300°.

In a small bowl, combine ground cookies, 1 tablespoon granulated sugar, and butter. Stir well. Press cookie mixture evenly into bottoms of 4 (4.5-inch) mini springform pans. Place on a baking sheet and bake for 7 minutes.

In the bowl of a stand mixer fitted with the paddle attachment, beat cream cheese, remaining ¾ cup granulated sugar, and vanilla at medium speed until well blended and smooth, stopping to scrape sides of bowl. At low speed, add eggs, one at a time, until just blended.

In a small bowl, combine 1 cup cream cheese mixture, pumpkin, brown sugar, cornstarch, and pumpkin pie spice; stir until well blended.

Alternately add spoonfuls of cream cheese mixture and pumpkin mixture evenly on top of crust in each pan. Using a knife, swirl batters together.

Bake until centers are almost set, about 40 to 45 minutes.

Run a metal spatula coated with cooking spray around sides of pans to loosen cakes from rims. Let cool 45 minutes on a wire rack. Remove rims and carefully transfer cakes to serving dishes. Garnish with whipped cream and sprinkle with pumpkin pie spice, if desired. Serve warm.