For crust, in a medium mixing bowl combine crushed gingersnaps, melted margarine or butter, and the 1 tablespoon flour. Press onto the bottom and about 1-1/2 inches up the sides of an 8- or 9-inch springform pan. Set pan aside.
For filling, in a large mixing bowl beat cream cheese until smooth. Add sugar, the 3 tablespoons flour, ginger, and vanilla; beat on high speed until smooth. Add eggs all at once. Beat on low speed just until combined. Stir in milk. Measure 2 cups of filling; set aside. To remaining mixture add pumpkin, brown sugar, cinnamon, and nutmeg.
Spoon plain cheese mixture into crust-lined springform pan. Carefully spoon the pumpkin mixture over plain cheese mixture. Use a spatula to gently swirl batters, being careful not to disturb crust. Place the springform pan on a shallow baking pan on the oven rack. Bake at 375 degrees F. for 50 to 55 minutes for an 8-inch pan (45 to 50 minutes for a 9-inch pan) or until center appears nearly set when shaken.
Remove springform pan from baking pan. Cool cheesecake on a wire rack for 15 minutes. Use a small metal spatula to loosen crust from sides of pan. Cool 30 minutes more. Remove sides of the springform pan. Cool for 1 hour; cover and chill at least 4 hours. Makes 12 to 16 servings.