FOR THE CAKE:
3 cups cake flour, spooned and leveled
1 3/4 cups granulated sugar
4 1/2 tsp. baking powder
1/2 tsp. salt
5 large egg whites
1 (13.66-ounce) can unsweetened coconut milk, divided
1 cup (2 sticks) unsalted butter, at room temperature
FOR THE FROSTING:
1 (8-ounce) package cream cheese, at room temperature
1/4 cup confectioners’ sugar
2 cup heavy cream, chilled and divided
1 1/2 c. toasted flaked coconut
Make cake: Preheat oven to 350°F. Coat three 8-inch round cake pans with nonstick cooking spray and line with parchment paper; coat parchment. Whisk together flour, sugar, baking powder, and salt in a bowl. Gently whisk together egg whites and 1/2 cup coconut milk until frothy in a second bowl.
Beat butter with an electric mixer on medium speed until smooth, 1 to 2 minutes. Gradually beat in remaining 1 cup coconut milk a little at a time, beating until light and fluffy, 2 to 3 minutes. Decrease mixer to low and add flour mixture and egg white mixture in three additions, beginning and ending with flour mixture, just until incorporated.
Transfer batter to prepared pans, dividing evenly (about 2 cups each). Bake until a toothpick inserted into centers comes out clean, 25 to 28 minutes. Cool in pans on wire racks, 10 minutes. Turn out onto wire racks to cool completely.
Make frosting and decorate: Whisk cream cheese and sugar with an electric mixer on medium speed until smooth, 2 to 4 minutes. Gradually add 1 cup cream until incorporated.
Beat until stiff peaks form, 1 to 2 minutes. Place one cake layer on a cake stand or plate. Top with half of frosting. Repeat one more time, then top with remaining layer.
Just before serving, whisk remaining 1 cup cream with an electric mixer on medium speed until stiff peaks form, 1 to 2 minutes. Frost top and sides of cake with whipped cream, then cover with toasted coconut.