Preheat the oven to 350 degrees. In a food processor, combine the gingersnaps and oil, and process until finely ground. Press the mixture onto the bottom of a 9-inch springform pan. Bake for 10 minutes, or until set and crisp. Leave the oven on.
In the same food processor bowl (no need to clean), combine the cream cheese, sour cream, pumpkin puree, brown sugar, whole eggs, egg whites, vanilla, cinnamon, ginger, cardamom, all-spice, and salt; process until smooth.
Pour the batter into the prepared pan. Sprinkle the walnuts over the batter. Bake for 1 hour.
Turn off the oven, prop open the oven door slightly, and let the cheesecake stand for 45 minutes in the turned-off oven. Cool to room temperature, then cover and refrigerate overnight.
Prepare this cheesecake the day before serving and refrigerate overnight.