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1
Preheat oven to 350F.
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2
Butter three 8- by 2-inch round cake pans and line bottoms with rounds of wax paper.
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3
Butter paper and dust with flour, knocking out excess flour.
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4
Into a bowl sift together flour, baking powder, and salt.
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5
In a glass measure stir together milk, water, and vanilla.
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6
In a large bowl with an electric mixer beat butter on medium speed 1 minute.
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7
Gradually beat in sugar and beat mixture until light and fluffy, about 2 minutes.
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8
Add eggs 1 at a time, beating well after each addition.
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9
With mixer on low speed add flour and milk mixtures alternately in 4 batches, beginning and ending with milk mixture, and beat until just combined (mixture will look curdled; do not overbeat).
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10
Divide batter evenly among pans (about 3 scant cups per pan), smoothing tops and tapping pans on counter to allow any air bubbles to escape.
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11
Bake layers in middle and lower thirds of oven (arrange pans so they overlap only slightly) until golden and a tester comes out clean, about 30 minutes.
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12
Run a thin knife around edges of pans and invert layers onto racks.
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13
Carefully remove wax paper and cool layers completely.
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14
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, layers may be made 3 days ahead and frozen, wrapped in plastic wrap and foil.
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16
Thaw layers in refrigerator 1 day before proceeding.)
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17
With a knife halve vanilla bean lengthwise.
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18
Scrape seeds into a 3-quart saucepan and stir in pod and remaining filling ingredients.
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19
Bring mixture just to a boil and cook at a bare simmer, stirring occasionally, 10 minutes.
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20
Discard pod and transfer filling to a bowl.
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21
Cool filling completely.
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22
Filling may be made 1 day ahead and chilled, covered.
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23
Bring filling to room temperature before proceeding.
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24
With a long serrated knife horizontally halve cake layers.
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25
Arrange 1 cake half, cut side up, on a cake plate and spread evenly with about 1/2 cup filling.
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26
Repeat layering in same manner with remaining cake halves and filling, ending with a cake half, cut side down.
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27
In a 3-quart metal bowl set over a saucepan of simmering water whisk together frosting ingredients until mixture is warm and sugar is dissolved.
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28
With a hand-held electric mixer on high speed beat frosting about 6 minutes, or until thick and fluffy.
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29
(Depending on mixer and weather, this may take longer.)
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30
Remove bowl from heat and beat frosting until cool and spreadable.
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31
Frost cake and coat with coconut.
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32
Cake keeps, covered, 2 days.
