Preheat the oven to 350°F (175°C). Coat two 9-inch round cake pans with baking spray and line the bottoms if desired.
Whisk the egg whites with 1/4 cup of the buttermilk until lightly combined. Set aside.
Beat the butter, sugar, vanilla, and almond extract on medium speed for 2 minutes, scraping the bowl as needed.
Add the cake flour, baking powder, and salt and mix until combined. Beat in the egg-white mixture, then add the remaining buttermilk. Beat for 3–4 minutes, scraping the bowl.
Fold in 1 cup shredded coconut. Divide the batter evenly between the prepared pans.
Bake for 26–28 minutes, until a tester comes out clean. Cool completely on wire racks.
For the frosting, beat the butter and cream cheese for 3 minutes. Add the powdered sugar and heavy cream and beat for 4–5 minutes, scraping the bowl as needed.
Place one cooled layer on a cake stand and spread with frosting. Add the second layer and frost the top and sides.
Press the remaining shredded coconut gently over the top and sides. Slice and serve.