Preheat your oven to 350°F. Grease three 8-inch round cake pans, line the bottoms with parchment paper, and grease the sides. If you have bake-even strips, use them for more even layers.

In a large bowl, beat together the granulated sugar, vegetable oil, melted butter, whole eggs, egg whites, and sour cream on medium speed until the mixture is lighter in color and well combined, about 2 minutes. Scrape down the bowl as needed.

In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. With the mixer on low, add half the dry ingredients, then the coconut and vanilla extracts, then half the coconut milk, mixing just until incorporated. Repeat with the remaining dry ingredients and coconut milk. Use a spatula to fold the batter from the bottom to ensure everything is evenly mixed.

Divide the batter evenly among the three prepared pans (about 1 2/3 cups per pan). Bake for 20 to 24 minutes, rotating the pans halfway through, until a toothpick inserted into the center comes out clean.

Let the cakes cool in the pans for 10 minutes, then turn them out onto a wire rack to cool completely. While the cakes cool, spread the 2 cups of shredded coconut for the topping on a parchment-lined baking sheet and toast in the oven for 5 to 8 minutes until golden. Transfer to a bowl to cool.

In a small bowl, whisk together 3 tablespoons of the heavy whipping cream with the cornstarch until smooth. Set aside.

In a medium saucepan over medium heat, melt the 1/2 cup butter. Add the remaining heavy whipping cream, 3/4 cup sugar, and the 2 1/4 cups shredded coconut. Stir occasionally and heat until the mixture is just about to boil.

Stir in the cornstarch mixture and continue cooking over medium-high heat, stirring constantly, until the filling thickens. Remove from heat and whisk in the 1/4 teaspoon vanilla extract. Let the filling cool completely.

In a large bowl, beat the softened butter and cream cheese together on medium-high speed until smooth and creamy, about 2 minutes.

Gradually add the powdered sugar, one cup at a time, beating on low until incorporated. Add the vanilla extract and beat until the frosting is fluffy and smooth.

Place one cake layer on an 8- or 10-inch cake board. Pipe a ring of cream cheese frosting around the edge of the cake to create a dam.

Spread half of the cooled coconut filling inside the dam. Top with a second cake layer, pipe another frosting dam, and fill with the remaining coconut filling. Place the third cake layer on top.

Frost the top and sides of the cake with a thin layer of cream cheese frosting. Press the toasted shredded coconut into the frosting, covering the entire cake.

Refrigerate the cake for at least 30 minutes before slicing. Store any leftovers in an airtight container in the fridge for up to 3 days.