Preheat oven to 350 degrees F (180 C). Grease the bottom of a 10-inch springform pan.
Combine the eggs, sugar, vanilla, coconut, baking powder and flour in a medium bowl and spread in the bottom of the pan. Bake for 25 minutes, then remove from oven and set aside to cool slightly. Spread with 1/2 of the pineapple topping, reserving remaining topping for use later in the recipe.
Place cream cheese in the bowl of a heavy-duty stand mixer. Beat on low speed until smooth. Add the sugar and beat until combined. Add the cream of coconut, and beat again. Add the eggs, one at a time, beating after each addition until well incorporated. Add the rum and coconut and beat until just combined. Pour over prepared base and bake 1 hour and 15 minutes.
While the cheesecake bakes, combine the sour cream, remaining pineapple topping and the two eggs in a bowl. When the baking time is over, remove the cake from the oven and spread with the sour cream mixture, return to the oven and bake for 15 more minutes. Remove from the oven and cool at room temperature for 1 hour.
Place the remaining 1/2 cup of sweetened coconut in a glass pie plate and toast in the oven for 10 to 15 minutes, until it becomes golden. Sprinkle the toasted coconut around the outside of the cheesecake. Refrigerate until ready to serve.
Makes 12 to 16 servings.
You will need 2½ cups sweetened coconut, in all, for the recipe.
Date: November 3, 2004