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MAKE CUSTARD FILLING FIRST:.
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Combine first 4 ingredients in a medium saucepan; bring to a full boil over medium-high heat.
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Reduce heat to low, and simmer about 1 minute.
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Whisk together egg yolks in a large bowl until well combined.
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Whisk about 1 cup hot cream mixture into yolks to temper them, then pour yolk mixture back into saucepan.
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Cook over medium heat, whisking often, until slightly thickened, about 1 to 2 minutes.
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Remove from heat, and whisk in coconut, stirring until thoroughly combined.
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(As you stir, coconut will absorb custard, and filling will thicken.)
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Pour filling onto an 18- x 13-inch rimmed baking sheet, and spread evenly with a rubber spatula.
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Cover with aluminum foil, and chill at least 2 hours, or until cool.
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MAKE CAKE:.
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Preheat oven to 350F
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Butter three 8- x 2-inch round cake pans.
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Line pans with parchment paper; butter paper.
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Sift first 6 ingredients into a 10-quart bowl (or the largest you have).
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Stir until well combined.
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Whisk together buttermilk, eggs, vanilla, and 1 cup room-temperature water in a medium bowl until just combined.
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Immediately add to flour mixture, and whisk until smooth, scraping down the side of the bowl with a rubber spatula.
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Add butter, and whisk until well combined.
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Batter will be thin.
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Divide batter evenly among prepared pans, gently shaking pans to level batter if necessary.
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Bake 16 to 19 minutes or until cakes are springy to the touch, start to pull away from sides of pans, and a wooden pick inserted in the center comes out clean.
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ASSEMBLY:.
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Let cakes cool in pans on cooling racks for 10 minutes, then invert onto racks, remove pans and parchment, and invert again so cakes are right side up.
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Place 1 cake layer on an 8-inch cardboard round or cake plate.
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Using a stiff offset metal spatula (the blade bends up where it meets the handle), spread one-third of chilled Custard Filling evenly over the top of the layer.
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(If filling seems too stiff, gradually stir in heavy cream to loosen it a bit.)
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Top with second cake layer, and spread another one-third of filling over the top.
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Place final cake layer on top, and spread with remaining filling, leaving sides bare.
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Sprinkle coconut over cake.
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Cover loosely with plastic wrap, and refrigerate until ready to serve, up to 2 to 3 days.
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Slice into hearty wedges, and serve a little cooler than room temperature.
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*After baking, cake layers can be assembled as described above or wrapped tightly in plastic wrap and chilled up to 1 day or frozen up to 1 month.
