Combine heavy cream, butter, and sugar in a saucepan.

Heat over medium heat until the sugar dissolves and the cream comes to a simmer. Do not boil. Remove from heat.

Add 20 ounces of chocolate and whisk until melted and smooth.

Mix in rum and vanilla extract.

Transfer one cup of this mixture to a small bowl, adding 2 ounces of chocolate to it for the glaze. Mix until smooth and set aside.

Pour the remaining mixture into a larger bowl for the filling. Chill until cold and thick, at least 6 hours or overnight.

Bring water and sugar to a boil, then remove from heat and let cool. Mix in the rum.

Preheat oven to 350°F. Line a 9x9" pan with parchment paper and butter the paper.

In a bowl, combine flour, cocoa powder, baking soda, and coffee powder.

In another bowl, beat egg yolks and ½ cup sugar with an electric mixer until thick and light in color. Beat in the vanilla extract.

In a separate bowl with clean beaters, beat egg whites and salt until soft peaks form. Gradually add remaining ¼ cup sugar, beating until stiff but not dry.

Fold half of the egg whites into the yolk mixture, then fold in half of the flour mixture. Repeat with remaining egg whites and flour mixture.

Transfer batter to the prepared pan and spread evenly. Bake for about 18 minutes until a toothpick inserted into the center comes out clean.

Cool in the pan on a rack. It might shrink slightly.

Cut around the pan to loosen the cake and turn it out onto a work surface. Peel off the parchment paper.

Using a long serrated knife, cut the cake horizontally in half. Place one half, cut side up, on a platter.

Brush the surface with syrup using a pastry brush.

Beat the cold chocolate ganache with an electric mixer until thick and lighter in color, about a minute. Do not overbeat.

Spread the filling evenly over the cake layer.

Brush the cut side of the other half with syrup and place it on top of the ganache layer, cut side down.

Rewarm the reserved cup of ganache over low heat until pourable. Pour it over the top of the cake, starting in the center. Use a spatula to spread it to the edges without spilling over.

Chill the cake overnight, covering loosely with foil or a cake dome after two hours.

Keep refrigerated but serve at room temperature.