In a large mixing bowl, beat cheese and sugar until creamy. Add eggs, 1 at a time, beating well after each addition. Add sour cream, liqueur and vanilla extract; beat until blended. Pour over crust. Bake in a 325° F oven until center of cake jiggles only slightly when gently shaken, 45 to 50 minutes. Cool completely on a rack. (If made ahead, cover and chill up until the next day.)
Spoon about 1/3 of the lukewarm Orange Sauce over cheesecake, to within 1 inch of sides. Peel mango. Cut fleshy cheeks off each side of pit, then cut off remaining fruit. Cut mango into thin slices 4 to 5 inches long. Arrange over cheesecake, overlapping slightly. Spoon remaining sauce over fruit and cake to within about 1/4 inch of side. Cover; chill until sauce is set, about 30 minutes or up to 8 hours. Run a knife around inside edges of pan. Remove pan rim. Garnish with mint. With a sharp knife, cut cake into wedges.
Mix 1 1/2 cups finely crushed crisp coconut macaroon cookies with 1/4 cup - 1/3 lbs) melted butter or margarine.
Press mixture over bottom and about 1 inch up sides of a 9-inch cheesecake pan with removable rim. Bake in a 325° F oven until lightly browned, about 15 minutes.
In a 2- to 3-quart pan, mix 3 Tbsp sugar and 4 tsp cornstarch.
Stir in 2/3 cup orange juice and 3 Tbsp orange-flavored liqueur (or orange juice). Stir over high heat until boiling. Cool to lukewarm.Makes 12