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Preheat the oven to 350°F. Lightly grease a 9" x 5" loaf pan.
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To make the cake: Beat the butter at medium speed, using an electric hand mixer or stand mixer, for about 10 seconds. Gradually add the sugar, beating all the while. Beat for 2 to 3 minutes, stopping to scrape down the sides and bottom of the bowl midway through, until the mixture has lightened in color and is fluffy. See our creaming butter and sugar video for a great demonstration of this technique.
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Add the eggs one at a time, beating each in completely before adding the next. Scrape the bottom and sides of the bowl, and beat briefly, just until combined; the mixture will look curdled.
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Beat in the salt, baking powder, coconut flavor, and vanilla.
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Add the flour to the bowl in three portions, alternating with the cream, and beginning and ending with the flour. Beat at low speed, just to combine, after each addition.
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Stir in the flaked coconut. Scoop the batter into the pan, smoothing its top surface.
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Bake the cake for about 70 to 75 minutes, until a toothpick inserted into the center/top of the loaf comes out clean. Tent it gently with aluminum foil for the final 15 minutes of baking, if it appears to be getting too brown.
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Remove the cake from the oven, let it cool in the pan for a couple of minutes, then turn it out onto a rack to cool completely.
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To make the frosting: Mix the butter and cream cheese at low speed, until thoroughly combined. Gently beat in the sugar, salt, and coconut flavor, until smooth.
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Place the cake on a large piece of waxed paper or plastic wrap. Spread the frosting all over the cake. Pat the flaked coconut onto the frosting. This will be sticky work; use the paper or wrap to help.
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Serve the cake in 1/2" to 3/4" slices. Store any leftovers, well-wrapped, in the refrigerator for 24 hours. Freeze for longer storage.