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1
Preheat oven to 350F.
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2
Butter an 8-inch square, 2-inch deep baking pan and line bottom with wax paper.
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3
Butter paper and dust with flour, knocking out excess flour.
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4
On a baking sheet toast coconut in the middle of the oven, stirring once, until golden, about 6 minutes.
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5
Into a bowl sift together flour, baking soda, baking powder, and salt.
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6
In a small bowl whisk together eggs, bananas, creme fraiche or sour cream, and vanilla.
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7
In a bowl of a standing electric mixer beat together butter and sugar until light and fluffy.
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8
Beat in flour and egg mixtures alternately, beginning and ending with flour mixture and beating after each addition until batter is smooth, and fold in coconut.
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9
Turn batter into pan, smoothing top, and bake in middle of oven until a tester inserted into center comes out clean, about 30 minutes.
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10
Cool cake in pan on rack 10 minutes.
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11
Run a thin knife around edges of pan and invert cake onto rack.
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12
Remove wax paper carefully and cool cake completely.
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13
Cake layer may be made 3 days ahead and chilled, wrapped in plastic wrap and foil.
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14
In a small saucepan bring water and sugar to a boil over moderate heat, stirring until sugar is dissolved, and simmer 1 minute.
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15
Stir in rum and simmer 1 minute.
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16
Cool syrup completely.
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17
Syrup may be made 3 days ahead and chilled, covered.
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18
In a bowl with an electric mixer beat together cream cheese and butter until light and fluffy.
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19
Add confectioners' sugar, 1/2 cup at a time, beating well after each addition, and beat in vanilla and pinch salt.
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20
In a food processor coarsely grind banana chips and stir into frosting.
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21
With serrated knife halve cake layer horizontally and with pastry brush dab cut sides with rum syrup, using it all.
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22
Spread half of frosting on cut side of bottom layer and arrange top layer, cut side down, on frosting.
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23
Spread remaining frosting on top of cake.
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24
Cake may be assembled 3 hours ahead and chilled, covered with an overturned bowl or in a cake keeper.
