To prepare the filling and the topping:
Stir the first three ingredients in a heavy, large saucepan over medium-high heat until the sugar dissolves and the cream starts to simmer. Take off the heat. Add 20 ounces of chocolate and whisk it until it’s smooth and melted.
Whisk in rum and vanilla. Move 1 cup of the warm chocolate mixture to a small bowl. Whisk the other 2 ounces of chocolate into the small bowl’s mixture, and set the bowl aside for the topping.
Cover and let the food sit at room temperature. Place the rest of the chocolate mixture in a large bowl to use as the filling. Put it in the fridge for at least 6 hours and up to a day, or until it is cold and thick.
For syrup:
In a small saucepan, stir water and sugar over low heat until sugar dissolves. Remove from heat and stir in the rum. Cover and allow to stand for 1 day.
For cake:
Preheat oven to 350 degrees Fahrenheit. Butter 9x9x2-inch metal baking pan. Line the bottom with butter paper or waxed paper. In a cup, combine vanilla and coffee powder; stir to dissolve the coffee. Flour, cocoa, and baking soda are sifted into a small bowl. In a medium bowl, beat egg yolks and 1/2 cup sugar with an electric mixer until very thick and pale, about 3 minutes. Blend in the coffee-vanilla mixture.
In a large bowl, beat egg whites, cream of tartar, and salt with clean, dry beaters until soft peaks form. Add the remaining sugar gradually while beating until stiff but not dry. Fold a third of the whites into the yolk mixture. Fold in fifty percent of the flour mixture. Fold in half of the remaining whites, then the remainder of the flour mixture, and finally the remaining whites. Transfer batter to the prepared pan and spread evenly with a spatula.
Bake for 18 minutes, or until the cake is puffed and a tester inserted into the center comes out clean. Cool in dish on a rack (cake may shrink slightly).
To release the cake from the pan, cut around the perimeter. Spread out on a tabletop and remove the paper. You should slice the cake in half horizontally using a long, serrated knife. Arrange 1 half on the platter, cut side up. Use about 3 and a half tablespoons of the syrup and drizzle it on top.
In less than 1 minute, using an electric mixer, beat the cold chocolate filling until thick and lighter in color. Evenly distribute the filling over the cake layer, making sure the edges are covered (filling will be about 1 inch thick).
The second cake layer should have the remaining syrup poured over the cut side. Cover the filling with the next layer, syrup side down, and press to secure. Gently reheat the topping until it can be poured again.
Place topping in the middle of the cake’s top. Spread the topping to the edges with the spatula, being careful not to let it overflow. Cover loosely with foil or a cake dome after 2 hours and refrigerate for up to 1 day.
Divide the cake into 16 equal squares before serving.
Notes
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