Preheat oven to 375°F. Stand a mixing bowl over the bottom part of a double boiler filled with steaming water. Beat the egg whites and ¾cup granulated sugar over steam until so stiff a spoon will stand in them. Remove from heat, and mix in the ground almonds.
Butter a 7-inch torte pan 3inches high with 1tablespoon butter. Dust with fine bread crumbs. Pour in the mixture. Bake the torte in the preheated oven for 15 to 20 minutes.
Cool the cake. Cut it into 2 layers.
Make the filling: Mix the egg yolks with the vanilla sugar and the powdered cocoa. Continue mixing and add milk and finally the rum.
Place the mixture over low heat and beat constantly until it starts simmering. Remove from heat.
Whip 6tablespoons of the butter till foamy, and mix it into the egg-yolk mixture.
Spread some of the filling on one cake layer. Place the other layer on top, then use the rest of the filling to spread on the sides.
Brown 5tablespoons granulated sugar with ½tablespoon butter till it is caramelized. Dip the whole almonds into the caramel. Work very fast; use alittle spoon or pincers to hold the almonds. Add 1teaspoon butter and stir again.
Place 1cup granulated sugar in a heavy frying pan and pour in 7ounces chopped almonds. Let the sugar melt and lightly brown; then pour it on marble or on a buttered cookie sheet and let it cool. Crush the candylike sheet in a mortar; the texture should be somewhat like that of uncooked rice. Sprinkle the top of the torte with the crushed almond caramel.
Place almonds on top of cake, making a circular design. Keep chilled but serve at room temperature.