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Preheat the oven to 350 degrees. Spray a 13- by 9-inch baking dish with cooking spray and set aside.
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Combine the cake mix, water, eggs, oil, and coconut extract in a large mixing bowl. Beat with an electric mixer on medium until smooth, 2 or 3 minutes.
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Pour into the baking dish and bake 22 to 32 minutes, until a cake tester inserted into the center of the cake comes out clean.
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Cool on a wire rack for 20 minutes.
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Use the handle of a wooden spoon to poke holes about 3/4 of the way into the cake (you don’t want to poke through to the bottom). The holes should be about 1 inch apart.
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Pour sweetened condensed milk evenly over the cake, then pour the cream of coconut over that. Gently smooth the condensed milk and cream of coconut over the cake so the whole top is covered.
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Cool to room temperature, cover loosely, and refrigerate overnight.