Preheat the oven to 350°F (175°C). Grease two 9-inch round cake pans with butter or nonstick spray. Line the bottoms with parchment rounds, then grease and lightly flour the parchment to help the layers release cleanly.

In a medium bowl, whisk together the cake flour, baking powder, baking soda, and fine sea salt. Stir in the very finely chopped unsweetened shredded coconut until evenly distributed. Set aside.

In a large mixing bowl (or stand mixer fitted with the paddle attachment), beat the softened butter and neutral oil together on medium speed until smooth, about 1–2 minutes. Add the granulated sugar and beat for another 2–3 minutes until the mixture looks pale and slightly fluffy.

Beat in the eggs one at a time, mixing well and scraping down the bowl as needed. Add the vanilla extract and coconut extract and mix until combined. The batter may look slightly curdled at this stage; it will smooth out once the dry ingredients and coconut milk are added.

With the mixer on low speed, add one-third of the flour mixture, then half of the coconut milk. Add another third of the flour mixture, then the remaining coconut milk, and finish with the last third of the flour mixture. Mix just until combined after each addition and stop as soon as no dry flour remains to avoid overmixing.

Divide the batter evenly between the two prepared cake pans and smooth the tops. Bake for 24–30 minutes, or until the tops are lightly golden and a toothpick inserted in the center comes out with just a few moist crumbs. Rotate the pans halfway through baking if your oven has hot spots.

Let the cakes cool in the pans for about 10 minutes. Run a thin knife around the edges, then invert onto wire racks. Peel off the parchment and allow the layers to cool completely before frosting.

In a large bowl, beat the softened butter and cream cheese together on medium speed until creamy and smooth, about 2–3 minutes. Add 3 cups of powdered sugar, the coconut milk, vanilla extract, coconut extract, and a pinch of salt. Beat on low until combined, then increase to medium and beat until fluffy. Add additional powdered sugar, about 1/2 cup at a time, until the frosting is thick, spreadable, and holds soft peaks without slumping.

If the cake layers are domed, use a serrated knife to level the tops. Place one layer on a serving plate or cake stand. Add a generous scoop of frosting and spread it evenly to the edges. Place the second layer on top. Spread a thin layer of frosting over the top and sides of the cake to create a crumb coat. Chill the cake for 20–30 minutes to let the crumb coat firm up.

After chilling, spread the remaining frosting evenly over the top and sides of the cake. Gently press sweetened shredded coconut onto the sides of the cake and sprinkle more on top to fully cover. Use a baking sheet underneath to catch any falling coconut, if desired.