Make the cake: Preheat the oven to 350˚ F. Butter the bottom and sides of two 9-inch round cake pans. Line the bottoms with parchment paper and butter the parchment. Flour the pans and tap out the excess.
Mix the coconut milk, water, vanilla bean paste and coconut extract in a liquid measuring cup. Whisk the flour, baking powder and salt in a medium bowl. Beat the butter and 1 cup granulated sugar in a large bowl with a mixer on medium-high speed until fluffy, 5 to 7 minutes. Reduce the speed to low; beat in the flour mixture in two batches, alternating with the coconut milk mixture. Increase the speed to medium high; beat until smooth, 30 seconds to 1 minute.
Beat the egg whites in a clean bowl with a mixer on medium-high speed until foamy. Gradually beat in the remaining 1/3 cup granulated sugar until stiff glossy peaks form, 5 minutes. Fold half the egg whites into the batter, then fold in the rest. Divide the batter between the prepared pans and smooth the tops, then tap the pans against the counter to remove any air bubbles.
Bake the cakes until the centers spring back when gently pressed, 30 to 35 minutes. Transfer to a rack and let cool 15 minutes in the pans. Loosen the edges with a knife and turn out the cakes onto the rack; remove the parchment and let cool completely.
Meanwhile, make the frosting: Beat the cream cheese, butter and salt in a large bowl with a mixer on medium-high speed until creamy, about 3 minutes. Reduce the speed to low; beat in half of the confectioners' sugar until combined. Beat in the remaining confectioners' sugar and the coconut extract. Increase the speed to medium high and beat until fluffy, about 3 minutes. Remove 1 cup frosting to a separate bowl; mix in the shredded coconut.
Put one cake on an 8-inch cardboard round. Spread the shredded coconut frosting on top, then top with the second cake. Spread a thin layer of the regular frosting over the top and sides of the cake (some crumbs are fine). Refrigerate 30 minutes, then cover with the remaining frosting, making it as smooth as possible. Refrigerate overnight or freeze for 2 hours.
Make the mirror glaze: Sprinkle the gelatin over 1/4 cup water in a small bowl; stir and set aside 5 minutes. Combine 3/4 cup water, the granulated sugar and condensed milk in a saucepan. Bring to a simmer, stirring to dissolve. Remove from the heat, add the gelatin mixture and stir to dissolve.
Pour the hot gelatin mixture over the white chocolate chips in a heatproof bowl; let stand 5 minutes, then whisk until melted. Strain through a fine-mesh sieve. Divide between two small bowls; tint one white and one blue. Let sit, stirring occasionally, until thickened and a thermometer registers 90˚ F.
Pour half of the white glaze into a medium bowl, then pour one-third of the blue glaze into the center. Pour half of the remaining white glaze into the center of the blue to create a bull’s-eye. Set aside the remaining glazes for touch-ups.
Position the cake (on the cardboard) on a small upside-down bowl set on a rimmed baking sheet. Starting along the outer edge, slowly pour the glaze in circles around the cake, working your way toward the center, until the cake is covered, letting the excess drip down the sides. Touch up any bare spots with the remaining glazes; sprinkle with edible glitter. Let stand until the dripping stops, about 30 minutes. Refrigerate until set, 1 to 3 hours.