Preheat oven to 400°.
To prepare crust, lightly spoon flour into dry measuring cups; level with a knife. Place 2/3 cup flour and 2 tablespoons sugar in a food processor; pulse until combined. Add butter; pulse 3 times or until the mixture resembles coarse meal. With processor on, pour ice water through chute, processing just until blended (do not form a ball). Press into bottom of a 9-inch springform pan coated with cooking spray. Bake at 400° for 8 minutes or until lightly browned. Cool on a wire rack. Reduce oven temperature to 325°.
To prepare filling, combine cocoa, fudge topping, and milk in a small bowl. Beat cheeses at high speed of a mixer until smooth. Add 1 1/2 cups sugar, 3 tablespoons flour, and extracts. Add eggs and egg whites, 1 at a time, beating well after each addition. Add chocolate mixture; beat well.
Pour cheese mixture into prepared pan. Bake at 325° for 1 hour and 5 minutes or until almost set. Cheesecake is done when the center barely moves when pan is touched. Remove cheesecake from oven; run knife around outside edge. Cool to room temperature.
To prepare the topping, combine caramel sundae topping, chopped pecans, and toasted coconut; spread over cheesecake. Cover cheesecake, and chill at least 8 hours.