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Preheat the oven to 375 degrees. Spray 3 8-inch round baking pans with cooking spray and line the bottoms with parchment paper. Spray the paper with cooking spray and set pans aside.
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Sift the flour, baking powder, baking soda, and salt together in a medium mixing bowl. Set aside.
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Place the butter, sugar, and cream of coconut in a very large mixing bowl and beat with an electric mixer set to medium speed until fluffy.
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Beat in the eggs, vanilla, and coconut extract to combine. Scrape down the sides and bottom of the bowl and add the milk, then beat until well combined.
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Turn mixer to low and beat in the dry ingredients until just incorporated. Scrape down the sides and bottom of the bowl again and stir with the spatula a few times to ensure all of the flour is mixed in.
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Divide the batter between the prepared pans and bake for 24 to 30 minutes, until a cake tester inserted into the center of the cakes comes out clean.
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Cool cake layers in pans for 20 minutes, then run a knife around the edge of the cake and carefully invert onto wire racks to cool completely before filling and frosting.