Preheat the oven to 350°F. Line the bottoms of two 9-inch round cake pans with parchment paper and grease the sides.

In a medium bowl, whisk together 2 cups all-purpose flour, 2 teaspoons baking powder, and 1 teaspoon salt. Set aside.

In a large bowl, beat 1 cup softened butter and 2 cups granulated sugar on medium-high speed for 3 to 4 minutes until light and fluffy.

Add 5 egg yolks one at a time, beating well after each addition, then beat for 1 minute until smooth.

Add half of the flour mixture to the butter mixture and beat on low until just combined. Pour in 1 cup coconut milk, 1 teaspoon coconut extract, and 1 teaspoon vanilla extract, then beat until incorporated. Add the remaining flour mixture and beat until the batter comes together. Fold in 1 cup sweetened shredded coconut.

In a separate clean bowl, beat 5 egg whites on high speed until stiff peaks form, about 3 to 4 minutes.

Gently fold the whipped egg whites into the batter in two additions using a rubber spatula and a folding motion.

Divide the batter evenly between the prepared pans and tap the pans on the counter to release air bubbles. Bake for 30 to 35 minutes, or until a tester inserted into the center comes out with just a few moist crumbs.

Remove the cakes from the oven and let them cool in the pans on wire racks for 15 minutes. Then turn the cakes out onto the racks and cool completely, about 60 minutes.

To make the frosting, beat 1 cup softened butter on medium-high speed for 2 minutes until creamy. Gradually add 4 cups powdered sugar, one cup at a time, beating well after each addition. Add 1/4 cup coconut milk, 1 teaspoon vanilla extract, 1/2 teaspoon coconut extract, and a pinch of salt. Beat on medium-high speed for 2 to 3 minutes until light and fluffy.

Assemble the cake by placing one layer on a serving plate and leveling if necessary. Spread 1/2 inch of frosting over the top, place the second layer on top, and frost the top and sides with the remaining frosting. Press 3/4 cup sweetened shredded coconut onto the sides and top of the cake. Chill for 30 minutes before slicing.