Preheat oven to 325°F. Place a large shallow pan of water on bottom rack of oven. Spray 10-in. springform pan with vegetable pan spray.
For crust, in food processor, process cookies until fine (crumbs should measure 2 cups). Stir together crumbs, sugar and melted butter; press into bottom of pan. Bake 8 minutes; cool completely.
Reduce oven temperature to 250°F.
To prepare filling, in large bowl, beat cream cheese and sugar with electric mixer on medium speed until light and fluffy. Beat in eggs one at a time, scraping bottom and sides of bowl often. Beat in cream, vanilla and cornstarch until mixture is smooth. Set aside 4 cups of the batter. Add melted chocolate and icing color to remaining batter; mix until well blended. Measure out 1/4 cup red velvet batter; set aside. Pour remaining red velvet batter over crust, spreading evenly. Carefully spoon reserved plain batter over red velvet batter. Drop spoonfuls of reserved red velvet batter on top; swirl with a small spatula.
Bake on center rack of oven, above pan of water, 1 to 1-1/4 hours or until filling is set but still jiggles slightly in center when pan is gently shaken. Turn oven off and with door closed, allow cheesecake to remain in oven for 1 hour. Transfer to cooling grid to cool completely. Refrigerate 3-4 hours or overnight until cheesecake is firm.