Toast the Coconut: Preheat the oven to 325°F. Line a baking sheet with parchment paper and spread the 2 cups of sweetened flaked coconut evenly across it. Bake for 8–12 minutes, stirring every 3 minutes, until the coconut turns lightly golden brown. Remove from the oven and let it cool completely. Transfer to an airtight container and keep at room temperature until needed. Prepare the Eggs and Cake Pan: Separate the 5 eggs, placing the yolks in one bowl and the whites in another. Make sure both portions are kept separate for use at different stages. Preheat the oven to 350°F. Grease and flour only the bottom of a 9-inch springform pan. Beat the Egg Yolks: Place the egg yolks in a mixing bowl and beat with ¾ cup of the granulated sugar until the mixture becomes pale in color and approximately doubles in volume.
Add the Milk and Coconut Extract: Pour the ⅓ cup whole milk and 1 teaspoon coconut extract into the beaten egg yolk mixture. Stir until evenly incorporated.
Mix the Dry Ingredients: Add the 1 cup all-purpose flour, 1½ teaspoons baking powder, and ¼ teaspoon kosher salt to the yolk mixture. Mix until the ingredients are combined into a smooth cake batter.
Whip the Egg Whites: In a separate clean bowl, beat the egg whites with the remaining ¼ cup granulated sugar until stiff peaks form.
Fold the Egg Whites into the Batter: Gently fold one-third of the whipped egg whites into the cake batter to lighten it. Add the remaining egg whites and carefully fold until incorporated. Avoid overmixing, as the airy egg whites help create the cake's soft, fluffy texture. Bake the Cake: Pour the finished batter into the prepared springform pan and spread it evenly. Bake at 350°F for 35–40 minutes, or until a cake tester inserted into the center comes out clean.
Cool and Pierce the Sponge: Remove the cake from the oven and allow it to rest in the pan for 10 minutes. Using a large fork, poke holes across the top of the warm cake so the soaking liquid can penetrate the sponge.
Prepare the Three-Milk Mixture: In a large bowl, combine the 14-ounce can of sweetened condensed milk, 3 tablespoons heavy cream, and ½ cup of the liquid from the canned coconut milk. Reserve the thicker coconut cream from the can for the frosting. Add ½ teaspoon coconut extract and whisk vigorously until the mixture is thoroughly combined. Soak the Warm Cake: Slowly pour the prepared milk mixture over the warm cake while it remains inside the springform pan. Allow the cake to cool completely on a wire rack, then transfer it to the refrigerator until thoroughly cold.
Whip the Coconut Cream Frosting: Using a stand mixer fitted with a whisk attachment, beat the 1¾ cups cold heavy cream, ½ cup powdered sugar, and 2 heaping tablespoons reserved coconut cream. A chilled mixing bowl works best. Continue whipping until the frosting thickens and holds peaks. Fold in the Coconut: Gently fold the ¾ cup sweetened flaked coconut into the whipped cream until evenly distributed.
Release the Cake: Once the cake is completely chilled, carefully run a knife around its edges to loosen it from the springform pan. Remove the sides of the pan without disturbing the soaked cake.
Frost and Garnish: Spread the coconut whipped cream evenly over the top of the cake. Finish by sprinkling the completely cooled toasted coconut over the frosting.
Chill and Serve: Keep the finished cake covered in the refrigerator until ready to serve. Slice and enjoy chilled.
