Preheat your oven to 350º F and prepare two or three 8-inch round pans by greasing them and adding parchment paper liners.
Combine the flour, baking powder, baking soda, and salt in a small mixing bowl and whisk until evenly distributed.
Beat the softened butter and granulated sugar in a large bowl with an electric mixer until light and fluffy, about 1 to 2 minutes.
Add the eggs one at a time, beating well after each addition, then incorporate the sour cream and coconut milk.
Gradually add the dry ingredients to the wet mixture, mixing until just combined, being careful not to overmix.
Divide the batter evenly between the prepared pans and bake for 35 to 40 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cakes to cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.
For the frosting, beat the remaining butter and cream cheese together until smooth, then stir in a dash of vanilla and coconut extract if desired.
Frost the cooled cake layers and cover the entire exterior with sweetened shredded coconut.