• Preheat the oven to 350°F. Lightly grease and flour a 9x13-inch baking dish.

Make The Coconut Cake:

• In a medium mixing bowl, sift together the cake flour, baking powder, baking soda, and salt. Sift a second time, then set aside.
  
• In a clean bowl, using a hand mixer or stand mixer with the whisk attachment, beat the egg whites on medium-high speed until stiff, glossy peaks form. Set aside.
• In a large mixing bowl, beat the butter and sugar together on medium-high speed until light and fluffy, 3-4 minutes, scraping down the bowl as needed.
  
• Add the egg yolks one at a time, beating well after each addition.
  
• Mix in the vanilla and coconut extracts until smooth.
  
• With the mixer on low, add about 1 cup of the flour mixture and mix just until combined. Add about 1/2 cup of the coconut milk and mix just until incorporated.
  
• Continue alternating additions of the flour mixture and coconut milk, mixing on low and scraping the bowl as needed, until everything is just combined. Do not overmix.
  
• Using a large spatula, gently fold the beaten egg whites into the batter in 2-3 additions, turning the batter over itself until no streaks of egg white remain.
  
• Spread the batter evenly in the prepared baking dish. Bake for 25-30 minutes, or until the top is golden brown, the center springs back when gently touched, and a toothpick inserted in the center comes out clean.
  
• Remove from oven and transfer to a wire rack to cool completely in the pan, about 60-90 minutes.
  

Make The Coconut Buttercream Frosting:

• In a large mixing bowl or the bowl of a stand mixer, beat the butter on medium speed until smooth and creamy, about 1 minute.
  
• Add 4 tablespoons coconut milk and the coconut extract and beat until combined.
• Gradually add the powdered sugar, about 1 cup at a time, beating on low until incorporated, then on medium until smooth after each addition. If the frosting is too thick, add more coconut milk 1 teaspoon at a time until it reaches a smooth, spreadable consistency. Beat 1-2 minutes until light and fluffy.

Frost And Serve The Cake:

• Once the cake has cooled completely, spread the coconut buttercream evenly over the top and sprinkle with toasted coconut if desired.
  
• Slice and serve immediately or cover the pan tightly.