• Preheat your oven to 350°F (175°C). Prepare three 8-inch round cake pans by lining the bottoms with parchment paper and greasing the sides. If you prefer, you can also wrap the pans with bake-even strips for flatter cake layers.
• In a large mixing bowl, combine the granulated sugar, vegetable oil, melted butter, eggs, and sour cream. Beat the mixture on medium speed for about 2 minutes, or until it's well blended and becomes lighter in color. Scrape down the sides of the bowl as needed to ensure even mixing.
• In a separate bowl, whisk together all the remaining dry ingredients. Begin incorporating the dry ingredients into the wet mixture in stages—add half of the dry ingredients, followed by the coconut and vanilla extracts, and then half of the coconut milk. Mix just until the flour begins to blend in. Repeat with the remaining dry ingredients and coconut milk. Once everything has been added, use a spatula to scrape down the bowl and fold the batter gently to ensure it's evenly mixed from top to bottom.
• Evenly divide the batter between the three prepared pans, using about 1⅔ cups of batter per pan. Bake in the preheated oven for 20–24 minutes, rotating the pans halfway through for even baking. Check for doneness by inserting a toothpick into the center of each cake; if it comes out clean, the cakes are done. Remove the cakes from the oven and let them cool completely in the pans before removing.
• To prepare the toasted coconut, line a baking sheet with parchment paper and evenly spread the shredded coconut across the pan. Bake in the preheated oven for 5–8 minutes, or until golden brown and fragrant. Immediately transfer the toasted coconut to a bowl or plate to prevent over-toasting. Allow it to cool completely before using.

To make the filling:

• In a small bowl, whisk together 3 tablespoons of heavy whipping cream and the cornstarch until thickened and smooth. If the mixture is too thick, add a little more cream to loosen it into a pourable consistency.
• In a medium saucepan over medium heat, melt the butter and add the remaining heavy cream, sugar, and sweetened shredded coconut. Stir the mixture occasionally and heat it until it is just about to boil. Once near boiling, whisk in the cornstarch mixture. Continue to cook the filling over medium-high heat, stirring constantly, until it thickens. Remove from heat and stir in the vanilla extract. Let the filling cool completely before assembling the cake.

To make the frosting:

• Once the cakes and filling are completely cooled, prepare the frosting. In a large mixing bowl, beat the softened butter and cream cheese together on medium-high speed using a paddle attachment until smooth and creamy. Gradually add the powdered sugar, one cup at a time, mixing well after each addition. As the frosting thickens, blend in the vanilla extract until fully incorporated and the frosting reaches a spreadable consistency.

To assemble the cake:

• Divide the cooled coconut filling in half. Place one cake layer on an 8- or 10-inch cake board or serving plate. Using a piping bag fitted with a large round tip, pipe a dam of frosting around the outer edge of the layer to contain the filling. Spoon one portion of the coconut filling into the center and gently spread it out evenly. Place the second cake layer on top and repeat the process with the remaining filling and another dam of frosting. Add the final cake layer on top.
• Frost the top and sides of the cake with the cream cheese icing. A smooth but not overly thick layer of frosting is ideal. Press the toasted coconut gently into the frosting with your hands, making sure to cover the cake completely and evenly.
• Chill the assembled cake in the refrigerator for at least 30 minutes before serving to help the layers set. Store the cake in an airtight container in the refrigerator to keep it fresh and prevent it from drying out.