Preheat the oven to 350 degrees F (175 degrees C). Spray a 10-inch springform pan with cooking spray and wrap the outside with foil.

Pulse gingersnap cookies into fine crumbs in a food processor. Transfer to a medium mixing bowl. Pulse pecans in the same food processor bowl until finely ground. Add to the cookie mixture and mix in melted butter.

Press the cookie and pecan mixture into the bottom and halfway up the sides of the springform pan.

Bake in the preheated oven until golden brown on the edges, about 10 minutes. Cool on a wire rack. Reduce the oven temperature to 300 degrees F (150 degrees C).

Beat cream cheese with sugar in the bowl of a stand mixer fitted with the paddle attachment, stopping occasionally to scrape the sides of the bowl, until smooth and creamy, about 3 minutes. Add eggs 1 at a time, beating just until combined and scraping the sides of the bowl after each addition. Beat in vanilla extract.

Pour about 1/2 of the batter into a different bowl and set aside.

Add pumpkin puree and pumpkin spice to the batter in the stand mixer bowl and mix until combined.

Transfer 1/4 cup of the plain batter into a piping bag or plastic storage bag. Spread the rest over the pie crust. Top with the pumpkin cheesecake batter.

Pipe remaining plain batter into 5 concentric circles on the top of the cheesecake. Drag the tip of a toothpick or small knife out from the center of the batter to the edge, wiping it down between each pull, to create a spider web effect.

Place the springform pan in the bottom of a roasting pan; fill roasting pan halfway up with warm water to create a water bath.

Carefully transfer cheesecake to the oven and bake until edges are set, top is no longer shiny, and center is still a little jiggly, about 1 hour and 10 minutes.

Turn the oven off and prop the door open at least 4 inches. Leave the cheesecake in the oven for an additional 30 minutes.

Remove cheesecake from the oven and water bath. Run a knife around the edge to prevent sticking and cool on a cooling rack for 30 minutes more. Cover loosely and chill for at least 6 hours, or overnight.

Run a knife around the edge of the pan and carefully remove the sides of the springform pan. Slice and serve.