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1
Preheat oven to 350F.
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Line bottoms of three buttered 9- by 2-inch round cake pans with rounds of wax paper or parchment paper and butter paper.
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Dust pans with flour, knocking out excess.
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4
In a bowl whisk together flour, baking powder, and salt.
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In a glass measure stir together milk, coconut liquid or water, and vanilla.
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In a large bowl with an electric mixer beat butter on medium speed 1 minute and add sugar in a slow stream, beating.
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Beat mixture scraping bowl occasionally, until light and fluffy, about 2 minutes.
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Beat in eggs 1 at a time, beating well after each addition.
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Reduce speed to low and beat in flour mixture in 4 batches alternately with milk mixture, beginning and ending with flour mixture and scraping bowl occasionally, until batter is just combined (do not overbeat).
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Divide batter among pans, smoothing tops and tapping pans on counter to allow any air bubbles to escape.
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Bake cake layers in middle and lower thirds of oven (arrange pans so they overlap only slightly) until a tester inserted in center comes out clean, about 30 minutes.
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Run a thin knife around edges of pans and invert cake layers onto racks.
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Remove wax paper carefully and cool cake layers completely.
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Cake layers may be made 1 day ahead and kept, wrapped in plastic wrap, in an airtight container in a cool dry place.
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15
(Alternatively, cake layers may be made 5 days ahead and frozen wrapped in plastic wrap and foil.
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Thaw cake layers in refrigerator 1 day before proceeding.)
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In a heavy saucepan whisk together yolks, sugar, lime juice, cream, and butter and cook over moderately low heat, whisking constantly, 5 to 7 minutes, or until mixture just reaches a boil (do not let boil).
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Strain curd through a fine sieve into a bowl and stir in zest.
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Cool curd its surface covered with plastic wrap, and chill at least 4 hours and up to 2 days.
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20
Put 1 cake layer on a cake plate and spread evenly with about half of lime curd.
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Sprinkle with 1/2 cup shredded fresh or sweetened flaked coconut and chill 15 minutes.
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22
Repeat layering in same manner with another cake layer, remaining lime curd, and remaining 1/2 cup coconut and top with remaining cake layer.
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23
Chill cake 15 minutes.
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24
In top of a double boiler off heat or in a large metal bowl with a hand-held electric mixer beat together frosting ingredients until combined.
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In double boiler or in bowl set over a saucepan of boiling water beat mixture on high speed until it holds stiff glossy peaks, about 7 minutes.
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(Depending on mixer and weather, this may take longer.)
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Remove top of double boiler or bowl from heat and beat frosting until cool and spreadable.
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28
Frost cake and coat with shaved fresh or sweetened flaked coconut.
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29
Pierce softest eye of each coconut with a metal skewer or small screwdriver and working over a bowl shake coconut, draining liquid and reserving coconut for shredding or shaving (procedure follows).
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30
Makes about a scant 3/4 cup liquid.
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Preheat oven to 400F.
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Bake reserved drained coconuts in oven 15 minutes
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With a hammer or back of a heavy cleaver, break shells and remove meat, levering it out carefully with point of a strong knife or small screwdriver.
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Remove brown membrane with a sharp paring knife or vegetable peeler.
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35
In a food processor fitted with fine shredding blade shred coconut meat from about 1 coconut in batches or shred by hand on fine shredding side (small tear-shaped holes) of a 4 sided grater until you have about 1 cup, reserving remaining coconut meat for another use.
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With a vegetable peeler shave edges of coconut meat pieces until you have about 3 1/2 cups, reserving remaining coconut meat for another use.
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Coconuts may be shredded or shaved 1 day ahead and chilled in a sealable plastic bag.