To make the cake layers, preheat oven to 350˚F. Butter two 9-inch round cake pans. Line the bottoms with parchment paper. Coat with butter and dust with flour. In a bowl, using an electric mixer on medium-high speed, beat the butter and 1 cup of the sugar for about 5 minutes. add the egg yolks one at a time, beating for 20 seconds after each addition. On a piece of parchment paper, sift the flour, baking powder, and salt. Add to the butter mixture in 3 batches, alternately with the coconut milk, beginning and ending with the flour mixture. Beat in the vanilla and the coconut extract, if using.

​In a clean bowl, using clean beaters, beat the egg whites until they form soft peaks. Add the remaining 1/4 cup sugar 1 tablespoon at at time, beating until the whites hold their shape. Using a rubber spatula, stir one-third of the egg white mixture into the batter. Fold the batter into the remaining egg whites. Divide between the prepared pans. Bake until a toothpick inserted into the centers comes out clean, 28—32 minutes. Transfer to racks, let cool in the pans for 5 minutes, then invert onto the racks.

​To make the filling, in a saucepan over medium heat, combine 3/4 cup cream, the sugar, and the butter. Cook, stirring, until the butter melts. In a bowl, whisk together the remaining 3/4 cup cream and the egg yolks. Stir into the saucepan. Cook over medium heat, whisking, until thickened, about 10 minutes. Remove from the heat. Stir in the vanilla, pecans, and coconut. Let cool, stirring occasionally. Fold the pineapple, orange, and maraschino cherries into the filling.

​To make the icing, in a heavy saucepan over low heat, combine the sugar, salt, and 2/3 cup water. Stir until the sugar is dissolved. Raise the temperature to medium-high and bring to a rolling boil. Cook until a syrup forms and registers 230˚F on a candy thermometer. In a bowl, using an electric mixer on medium-high speed, beat the egg whites until they form soft peaks. When the sugar syrup has reached 240˚F, pour in a thin steady stream into the egg whites while beating on high speed. Beat until the frosting is cooled, thick, and glossy, about 7 minutes. Beat in the vanilla and the coconut extract, if using.

​Place 1 cake layer, top side down, on a serving plate. Spread with half of the cooled filling. Top with the second layer, top side up. Spread the top and the sides with icing. Press the flaked coconut onto the cake. Cover and refrigerate until ready to serve. Pass the remaining filling at the table.