Heat oven to 450°F. Make pie crust as directed on box for One-Crust Baked Shell using 9-inch glass pie plate. Bake 9 to 11 minutes or until light golden brown. Cool completely, about 30 minutes.
Meanwhile, in 2-quart saucepan, heat milk and pudding mix to a full boil over medium heat, stirring constantly. Remove from heat. Stir in chocolate chips until melted. Place plastic wrap directly over surface of pudding. Refrigerate 45 minutes or just until cooled.
In small bowl, beat cream cheese, powdered sugar, peppermint extract and food color with electric mixer on medium speed until smooth. On low speed, gradually beat in 1 cup of the whipped topping until combined. Spread in cooled baked shell.
Stir cooled pudding mixture; spread over cream cheese layer. Carefully spread remaining 1 cup whipped topping over pudding layer. Garnish with chocolate shavings. Refrigerate 1 hour or until chilled before serving. Store in refrigerator.