Pumpkin Cheesecake with Gingersnap-Walnut Crust

Preheat oven to 325 degrees F. Coat a 9-inch springform pan with cooking spray. Tightly wrap the outside of the pan bottom and sides with heavy-duty foil to help keep the water bath from leaking into the cake. Put a kettle of water on to boil for the water bath.

Grind cookies and 1/3 cup walnuts to a fine meal in a food processor. Drizzle in oil and process, scraping the sides as needed, until the crumbs are evenly moistened. Press the crumb mixture firmly into the bottom of the prepared pan. Place the pan in a roasting pan and set aside. Clean the food processor.

Beat cream cheese, granulated sugar, brown sugar and pumpkin pie spice in a large bowl with an electric mixer on medium-low speed until the spice is incorporated. Increase speed to medium-high and beat until completely smooth, scraping down the sides occasionally. Beat in eggs one at a time, scraping down the sides occasionally. Beat in vanilla.

Process cottage cheese in the food processor until completely smooth, about 2 minutes, scraping down the sides once. Gradually beat the cottage cheese and pumpkin puree into the cream cheese mixture on medium speed. Scrape down the sides and beat a final time to make sure no streaks remain. Pour the batter into the crust.

Pour enough boiling water into the roasting pan to come 1 inch up the side of the springform pan to create a hot water bath for the cake. Carefully transfer the roasting pan to the oven. Bake the cheesecake in the center of the oven until it's set around the edges but the center still jiggles slightly, 1 1/2 to 1 3/4 hours.

Remove the roasting pan from the oven. Let the cake cool in the water bath until the water is room temperature. Coarsely chop the remaining 2/3 cup walnuts. Toast them in a dry skillet over medium-low heat until fragrant, 3 to 5 minutes. Remove the pan from the water bath. Remove the foil. Place the nuts decoratively around the edge of the cheesecake. (Alternatively, turn the nuts into Candied Walnuts and decorate just before serving; see Variation.) Refrigerate, uncovered, until very cold, at least 4 hours. Wrap tightly and refrigerate overnight if desired.

To serve, remove the sides of the pan. Transfer the cheesecake to a cake stand, if desired.