Preheat and prepare pan. Preheat the oven to 325° F. Grease and flour three 8” cake pans. Set aside.
Combine wet ingredients. In a small mixing bowl, mix together the canned coconut milk, vegetable oil and melted butter. Set aside.
Sift dry ingredients. In a mixing bowl, whisk together the cake flour, baking powder, and salt. Set aside.
Mix eggs, sugar and extracts. In a large mixing bowl, with an electric hand mixer with whisk attachment, beat the eggs, sugar, vanilla, and coconut extract, until thickened and light gold in color, about 2 minutes at medium-high speed. If your stand mixer doesn’t have a whisk attachment, beat for 5 minutes using the paddle attachment. The batter should fall in thick ribbons from the beaters.
Alternate dry ingredients with coconut milk mixture. Add dry ingredients alternately with coconut milk mixture to the sugar and egg mixture, beginning and ending with the dry ingredients. Do not overmix once the last of the dry ingredients mixture has been added. Stir in shredded coconut.
Bake. Bake the cakes until a toothpick inserted into the center comes out clean and the top feels set, about 25-30 minutes. Remove the cakes from the oven, carefully loosen the edges, and allow them to cool for 10 minutes in the pans. Then turn them out of the pan and transfer them to a rack, right-side up, to cool to room temperature.