Pre-heat the oven to 350°F.
In a medium mixing bowl, toss together coconut, sugar and lime zest. Add butter and stir until crumbly. Press mixture into bottom of a 9-inch non-stick springform pan. Bake in preheated oven for 10 to 12 minutes, until light brown. Allow to cool while you prepare filling.
Reduce the oven temperature to 300°F.
In a large mixing bowl, with an electric mixer on medium speed, beat cream cheese until smooth. Gradually beat in sweetened condensed milk, beating until smooth. Add eggs, lime juice, vanilla extract and cornstarch, mixing until well combined.
Pour cheese mixture into prepared crust. Stir jam until smooth, drop dollops of jam on top of filling. Gently swirl jam with a knife until top of filling appears marbleized.
Bake in pre-heated oven for 55 to 60 minutes, or until center is set when jiggled. Place pan on wire rack to cool completely. Cover and refrigerate 8 hours to overnight.
To serve:
Run a knife along inside edge of spring-form pan, remove side of pan. Place cake on serving platter. Garnish with alternating slices of mango and lime. Serve sliced cake with sweetened whipped topping, if desired.
*You may substitute the sweetened condensed milk with the following option:
2 eggs
1 cup brown sugar
1 teaspoons vanilla
2 tablespoons flour
1/2 teaspoons baking powder
1/4 teaspoons salt
Mix all ingredients and use as a substitute for sweetened condensed milk in recipes for pies, bars and desserts.
From cooks.com
**I like using the Oxygen brand mango jam for this cake. Pineapple or peach jam may be substituted.