Cake: Preheat the oven to 400 degrees F. Mark the outline of a 9-inch cake pan on parchment paper. Repeat until you have 6 marked circles.
Place butter and vanilla in mixing bowl. Warm over low heat to soften. Transfer to a mixer and whip for 1 minute. Add powdered sugar and continue to whip another 5 minutes, until smooth and well blended. Lower the speed and add the egg yolks. Continue to whip for 2 to 3 minutes, until light.
In another mixing bowl, whip the egg whites until soft peaks. Add the granulated sugar and increase speed of the mixer. Whip until stiff but not dry. Fold the meringue into the egg yolk mixture. Gently fold flour into the egg mixture. Divide the batter equally among the 6-marked circles. With an offset spatula, spread the batter about 1/4-inch thick to fill in the marked circle. Bake in preheated oven for 6 to 8 minutes or until light golden in color. Allow to cool. Transfer each cake circle onto a 9-inch cake board. Reserve.
Chocolate Buttercream: In a saucepan, combine the sugar and water. Boil to 240 degrees F or soft ball stage on a candy thermometer. Do not stir.
Meanwhile, in a mixer, beat the eggs and egg yolk until light and ribbony. Lower the speed and gradually pour the hot syrup into the egg mixture. Increase the speed and whip mixture until room temperature. Add the butter, 1 piece at a time. Then add the melted chocolate and rum, if desired. Continue to whip until smooth and well blended.
Caramel Topping: Cook sugar until is amber in color. Pour caramel over 1 of the reserved cake layers. Run edge of a chef's knife in butter. With the help of the buttered edge knife, spread the caramel to cover the entire surface of the cake circle. Allow to cool to set the caramel. Cut into 12 equal pie cuts. Reserve.
To assemble torte: Reserve half of the Chocolate Buttercream. Using some of the remaining buttercream, spread a 1/8-inch layer on top of the first cake layer. Continue layering the remaining the 4 remaining cake circles and spreading the buttercream. When all 5 cake layers have been frosted, frost the sides and top of the cake. Use a pastry comb to finish the sides of the layered cake. Mark the top of the cake into 12 pie sections. Pipe the remaining buttecream on top of each pie section and arrange the caramel slices on top of the piped cream at an angle.