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1
Preheat oven to 350F and butter 2 (8-inch) square cake pans (2 inches deep).
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2
Sift flour with salt into a bowl.
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3
Heat eggs and sugar in large metal bowl set over a pot of simmering water, gently whisking constantly, until lukewarm.
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4
Remove bowl from heat and add vanilla, then beat with an electric mixer at medium-high speed until thick and pale and tripled in volume (about 5 minutes with a standing mixer or 10 minutes with a hand held).
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5
Sift flour and salt over eggs in 2 batches, folding gently but thoroughly after each batch.
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6
Fold in melted butter until combined.
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7
Divide batter evenly between cake pans, smoothing tops.
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8
Bake cakes in middle of oven until a tester comes out clean and cakes are golden, about 15 minutes.
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9
Cool in pans on racks 5 minutes, then invert onto racks to cool completely.
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10
Stir together filling ingredients in a heavy saucepan until cornstarch is dissolved.
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11
Bring to a boil, stirring constantly, then simmer, stirring, 3 minutes.
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12
Cool filling completely, stirring occasionally.
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13
Bring water and sugar to a boil in a small heavy saucepan, stirring until sugar is dissolved.
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14
Remove from heat and stir in rum.
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15
Transfer to a small bowl and chill until ready to use.
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16
Trim edges of cakes if necessary and cut each horizontally in half with a long serrated knife to form a total of 4 thin layers.
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17
Put 1 cake layer, cut side up, on a cake plate and brush top with some rum syrup, then spread half of pineapple filling over it.
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18
Top with another cake layer and brush with syrup, then spread with about 2/3 cup butter cream.
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19
Top with a third cake layer and brush with syrup, then spread remaining pineapple over it.
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20
Top with fourth layer, cut side down, and brush with remaining syrup.
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21
Frost sides and top of cake with remaining butter cream, then coat with coconut.
