Heat oven to 350º. Generously butter a 9×2-inch round cake pan and line the bottom with a round of parchment paper. On a small baking pan, baking coconut for 8-12 minutes, stirring halfway through, until toasted. Set aside to cool.

In a medium bowl, whisk together the flour, baking powder and salt. Add the coconut and stir to combine. Set aside.

In the bowl of a stand mixer fitted with the paddle attachment, beat together butter, granulated sugar and lime zest on medium speed until light and fluffy. Add eggs one at a time, mixing well after each addition. Add 2 tablespoons lime juice to the milk and stir well. With the mixer on low speed, add flour and milk mixtures alternately in batches, beginning and ending with the flour.

Pour batter into prepared cake pan and smooth top. Bake until golden and a toothpick inserted in the center comes out clean, 40-45 minutes. Cool slightly in pan, then turn onto a wire rack. Brush with rum (about 1 tablespoon), if desired. Cool completely on the wire rack.

While the cake is cooling, prepare the coconut ribbons. Leave the oven on after removing cake. Pierce one eye of the coconut and drain coconut water. Save for another use. Bake coconut in a shallow baking pan for about 15 minutes. Using a hammer, break the shell and remove from flesh. Leave oven on.

Using a vegetable peeler, peel coconut into thin slices (enough for 2 cups). Toss with confectioners sugar and bake until dry but not toasted, 5-10 minutes. Set aside while you prepare the glaze.

To make glaze, whisk together confectioners’ sugar, remaining 2 tablespoons lime juice and rum. Slowly pour glaze over the cooled cake, then top with coconut ribbons and serve immediately.