1CAKE: Beat 3/4 cup sugar and the egg yolks until light and fluffy, about 5 minutes. Fold in the milk, vanilla, flour and baking powder.
Beat the egg whites to soft peaks, adding the cream of tartar after 20 seconds. Gradually add the remaining 1/4 cup sugar and continue beating until the whites are glossy and firm, but not dry. Gently fold the whites into the yolk mixture. Pour this batter into the buttered baking dish.
Bake the cake until it feels firm and an inserted toothpick comes out clean, about 40 to 50 minutes. Let the cake cool completely on a wire rack. Unmold unto a large, deep platter (*). Pierce the cake all over with a fork, taking care to not tear it up.
MILK SYRUP: Combine the evaporated milk, sweetened condensed milk, cream, vanilla and rum in a mixing bowl. Whisk until well blended. Pour the syrup over the cake, spooning the overflow back on top, until it is all absorbed.
MERINGUE: Place 3/4 cup plus 2 tablespoons of the sugar in a heavy saucepan with 1/4 cup water. Cover and cook over high heat for 2 minutes. Uncover pan and cook the sugar to the soft ball stage, 239oF on a candy thermometer, 6 to 8 minutes.
Meanwhile beat the egg whites to soft peaks with the cream of tartar. Add the remaining 2 tablespoons of the sugar and continue beating to stiff peaks. Pour the boiling sugar syrup in a thin stream into the stiff egg whites and continue beating until the mixture is cool to the touch. The hot syrup "cooks" the egg whites.
Using a wet spatula, spread the top and sides of the cake with a thick layer of the meringue. Refrigerate the cake for at least 2 hours before serving.