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1
In the bottom of an 8 1/2-inch springform pan arrange the cake, cutting the pieces to fit in one layer, and freeze it while making the ice cream.
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2
In a heavy saucepan combine pineapple and 1/4 cup of the sugar and simmer the mixture, stirring until the sugar is dissolved, for 5 minutes.
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3
Drain the pineapple mixture in a fine sieve set over a bowl, reserving the syrup for another use.
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4
In a bowl whisk together the remaining 1/2 cup sugar, the cornstarch, a pinch of salt, the yolks, and the whole egg and add the milk, scalded, in a stream, whisking.
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5
In a heavy saucepan bring the custard to a boil over moderate heat, whisking, boil it, whisking, for 2 minutes, and strain it through a fine sieve into a metal bowl set in a larger bowl of ice and cold water.
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6
Stir in the pineapple mixture and vanilla, let the custard cool, stirring, and stir in the cream.
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7
Freeze the custard in an ice-cream freezer according to the manufacturer's instructions until it is frozen but still soft.
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8
Spoon the ice cream over the cake, spreading it evenly, and freeze the cake while making the topping.
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9
In a bowl beat the cream until it holds soft peaks and beat in the sugar and sour cream.
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10
Beat the mixture until it just holds stiff peaks and fold in the coconut gently but thoroughly.
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11
Spoon the topping over the ice cream, spreading it evenly, and freeze the cake, its surface covered with plastic wrap, overnight.
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12
Let the cake stand at room temperature for 10 minutes, remove the side of the pan, and transfer the cake to a serving plate.
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13
Sprinkle the coconut on top and serve the cake into wedges.
