Be sure to use real peppermint extract instead of imitation flavoring.
Combine first 3 ingredients; stir well. Firmly press mixture into bottom and 1/2 inch up sides of a 9-inch springform pan. Bake at 325° for 12 minutes.
Beat cream cheese at medium speed with an electric mixer until creamy; gradually add 1 cup sugar, beating well. Add eggs, 1 at a time, beating after each addition and scraping sides and bottom as needed. Stir in sour cream and vanilla. Divide batter into thirds.
Microwave 1 cup mini-morsels at HIGH 1 minute or until melted and smooth; stir into one-third of cheesecake batter, stirring until combined. Add remaining mini-morsels to one-third of batter. Stir green food coloring and peppermint extract into remaining batter.
Pour melted chocolate batter into prepared crust; spoon mint batter gently over chocolate layer. Spoon chocolate morsel batter gently over mint layer. Bake at 325° for 1 hour and 5 minutes. Remove from oven; immediately run a knife around edge of pan, and release sides. Turn oven off, and partially open door; return cheesecake to oven, and cool in oven 45 minutes. Remove from oven; cool completely in pan on a wire rack. Cover and chill 8 hours or overnight. Store in refrigerator.