Combine gingersnaps, walnuts, sugar and butter in a medium bowl. Press into the bottom and 1-inch up the side of a 10-inch nonstick springform pan. Set aside.
Beat cream cheese, sugar and flour with an electric mixer until smooth. Add 5 eggs, one at a time, then vanilla, beating on low speed. Transfer 2-1/2 cups to a separate bowl; set aside. Beat 1 egg, pumpkin pie spice and pumpkin into remaining filling until smooth. Pour half of pumpkin filling into crust, then half of the plain; repeat. Swirl gently with a spoon.
Bake at 500 degrees F for 10 minutes; reduce temperature to 200 degrees F and bake for 30 minutes. Tent with aluminum foil and continue baking for 1 hour or until center appears nearly set. Run a knife around top of cake to loosen from pan.
Turn off oven and open door to allow cake to cool gradually for 20 to 30 minutes. Remove from oven and finish cooling on a rack for 15 minutes, then chill in refrigerator at least 6 hours
TIP: Place a pan of water in the oven with the cheesecake while baking. This will help prevent the cake from cracking.