allow butter and eggs to stand at room temperature for 30 minutes. Meanwhile, preheat oven to 325°. Coat a 10 inch fluted tube pan with spray for baking. Set aside.
In an extra-large bowl mix butter and shortening. Beat with electric mixer on medium to high speed for 30 seconds. Gradually add sugar, beating on medium speed until light and fluffy. Add eggs, one at a time, beating on low to medium speed for one minute after each addition and scraping sides of bowl frequently.
In medium bowl stir together flour and baking powder. In a small bowl mix cream of coconut, lime juice, the water, and vanilla. Alternately add flour mixture and cream of coconut mixture to butter mixture, beating on low speed after each addition just until combined. Fold in flaked coconut.
Pour batter into prepared pan, spreading evenly. Bake for 65 to 75 minutes or until a toothpick inserted in center of cake comes out clean. Cool in pan on wire rack for 10 minutes. Remove from pan. Cool completely on rack.Drizzle lime icing over cake. If desired, sprinkle with toasted coconut shards. Makes 12 to 16 servings.
Lime icing: in a small bowl mix 1 cup powdered sugar, 1 tablespoon milk, 1/2 teaspoon finely shredded lime peel, and 1/4 teaspoon coconut extract. Stir in enough additional milk, 1 teaspoon at a time, to make of drizzling consistency.
To make toasted coconut shards, preheat oven to 350°. Using a vegetable peeler, shape curls of fresh coconut. Spread in a single layer in a shallow baking pan. Bake for 5 to 10 minutes or until light brown.