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1
Preheat the oven to 350 degrees and grease an 8 inch square cake pan or 9 inch round pan.
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2
To prepare the sponge cake, sift the flour and baking powder into a small mixing bowl.
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3
Using an electric mixer, beat the eggs and yolks at high speed for about 4 minutes, or until thick.
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4
Gradually add the sugar to the eggs and beat at medium speed for 4 or 5 minutes, until light and fluffy.
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5
Add the flour mixture to the eggs and beat at medium-low speed until just combined.
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6
Put the water and butter in a saucepan and stir over medium heat until the butter melts. Add to the batter and beat until combined.
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7
Pour the batter into the prepared baking pan. Bake in the over for 20 to 25 minutes, or until an inserted toothpick come out clean.
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8
Let the cake cool in the pan briefly, then remove and cool on a wire rack. Cover with plastic wrap or foil and place in the freezer, preferably overnight.
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9
To prepare the haupia, place the coconut milk, 1 cup of the water and the sugar in a saucepan and bring to a boil.
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10
Mix the cornstarch and the remaining 1 cup of water together in a bowl, add to the pan, and stir until the mixture returns to a boil and thickens. Remove from the heat and keep warm in a double boiler.
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11
Remove the sponge cake from the freezer and cut a thin slice off the top to level off the cake. Slice the cake in half horizontally to make two even layers. Pour the haupia over the bottom layer, to a thickness of about 1/2 inch.
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12
Place the top layer of cake over the haupia, gently pressing down. Pour more of the haupia over the top of the cake, using a spatula (or chill it in a small shallow pan, cut it into squares, and serve with the cake - or eat it before your company arrives!).
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13
Refrigerate the cake for 3 to 4 hours. When ready to serve, sprinkle the shredded coconut on top the cake.
