For the Cake:
2 cups all-purpose flour, sifted
4 teaspoons baking powder
6 large eggs, separated and at room temperature
1 teaspoon salt
1 1/2 cups sugar
1/2 cup milk, at room temperature
2 teaspoons pure vanilla extract
2 cups sweetened shredded coconut

For the Coconut Milk Bath:
2 (13.5-ounce) cans coconut milk
2 (14-ounce) cans sweetened condensed milk
1 cup heavy cream

For the Toasted Meringue Topping:
1 1/3 cups sugar
1/4 cup water
2 tablespoons light corn syrup
6 large egg whites, at room temperature
1/4 teaspoon salt
2 cups toasted sweetened shredded coconut (See Notes)