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Preheat the oven to 350°F. Lightly grease a 9" x 13" x 2" pan; line it with parchment and grease the parchment, if you plan on turning the cake out onto a serving platter. Note: Your pan must be at least 2" deep; this is a high-rising cake.
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To make the cake: Combine the egg whites and cream of tartar in a large bowl, and beat the whites until soft peaks form. Set them aside.
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In another large bowl, beat the egg yolks until well combined. Add the sugar, and beat until the mixture comes together and thickens. When you stop beating, the mixture should fall from the beater(s) in ribbons as you lift them out of the bowl.
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Add the water and vanilla and almond extracts to the egg yolk mixture, beating to combine.
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Stir in the baking powder, salt, and flour, beating just to combine.
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Gently and thoroughly fold in the beaten egg whites, stirring until no streaks of white show.
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Scoop the batter into the prepared pan, gently smoothing the top.
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Bake the cake for 28 to 30 minutes, until a toothpick inserted into the center comes out clean. Remove it from the oven, and set it on a rack. Loosen the edges with a spatula or table knife.
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After 20 minutes, gently turn the cake out onto a serving platter, turning it upright, if desired. You can also leave it face-down if you like; you'll be topping it with whipped cream, so any imperfections on the bottom crust will be hidden. You may also choose to serve the cake right from the pan; in which case, leave it where it is.
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Allow the cake to cool to room temperature.
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To make the topping: Combine the 1/2 cup cream, condensed milk, evaporated milk, and vanilla or liquor, stirring thoroughly.
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Poke the cake all over with a fork. Pour the milk mixture over the cake slowly, stopping occasionally to allow it to soak in. This seems like a lot of liquid for the cake to absorb; but don't worry, it will.
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Cover the cake and refrigerate it for several hours before serving.
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Just before serving, make the frosting: Whip 1 1/2 cups heavy cream with 1/4 cup sugar until the cream is stiff enough to spread. Spread the cream over the top of the cake, swirling it with your spatula. Dust with ground cinnamon, if desired. Serve with diced mango, pineapple, or other tropical fruits; or simply as is, in all its sweet glory.
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Storage information: Refrigerate any leftover cake for up to several days.