Preheat the oven to 350°F (175°C). Grease two 9-inch cake pans with cooking spray.

In a small bowl, whisk together 2¾ cups all-purpose flour, 1 teaspoon baking powder, ½ teaspoon baking soda, and ½ teaspoon salt. Set aside.

In a clean, dry bowl (free of any grease), beat 4 room-temperature egg whites with an electric mixer until stiff peaks form. Transfer the whipped egg whites to a separate bowl and set aside.

In a large mixing bowl, beat ½ cup softened butter, ½ cup coconut oil, and 1¾ cups sugar together on medium speed until light and creamy.

Beat in 1 cup cream of coconut, then beat in 4 egg yolks and 1 teaspoon vanilla extract until combined.

Add the dry ingredient mixture to the butter mixture in two additions, alternating with 1 cup buttermilk: add half the dry ingredients, then half the buttermilk, then the remaining dry ingredients, and finish with the remaining buttermilk. Beat only until just combined after each addition.

Gently fold the whipped egg whites into the batter in two additions, using a spatula and folding motions, until no white streaks remain. Do not overmix.

Divide the batter evenly between the two prepared 9-inch pans and smooth the tops. Bake for 30–35 minutes, or until a toothpick inserted into the center comes out clean.

Let the cakes cool in their pans for about 10 minutes, then invert onto wire racks and cool completely before frosting.

For the frosting, beat 4 ounces softened cream cheese and 5 tablespoons softened butter together until smooth and creamy.

Beat in ½ teaspoon coconut extract and 1 pinch salt. Gradually add 3 cups powdered sugar and beat until the mixture is smooth.

Add 1 to 2 tablespoons cream of coconut (start with 1 tablespoon, add up to 2 tablespoons as needed) and beat until the frosting reaches a spreadable consistency.

Level the top of each cake layer with a serrated knife if needed. Place one layer on a serving plate, spread about 1 to 1½ cups of the frosting evenly over the top, then place the second layer on top.

Spread the remaining frosting over the top and sides of the assembled cake. Chill briefly if desired to set the frosting before serving.