Prepare the Filling

1. Cook the Milk:
   • In a large saucepan, bring the milk, sugar, and vanilla extract to a boil.
2. Mix Cocoa and Flour:
   • In a separate bowl, whisk together a portion of the milk with the cocoa powder and flour until smooth.
3. Combine and Thicken:
   • Gradually add the cocoa-flour mixture to the boiling milk, stirring constantly. Add the dark chocolate and continue cooking until the mixture thickens.
4. Finish the Filling:
   • Remove from heat and immediately stir in the butter and rum. Mix until the butter is fully melted and the mixture is smooth. Cover with plastic wrap and let cool completely.

Make the Cake Layers

1. Prepare the Dough:
   • In a large mixing bowl, beat the butter, sugar, egg whites, and sour cream until fluffy.
   • Gradually add the sifted flour and baking powder, kneading until a smooth dough forms.
2. Divide and Roll:
   • Divide the dough into six equal parts.
   • Roll each part between two sheets of parchment paper into thin rectangles, sized to fit your baking tray.
3. Bake the Layers:
   • Preheat the oven to 356°F (180°C).
   • Bake each layer, one at a time, on a parchment-lined baking tray for about 8 minutes, or until set but still pale. Cool completely on a wire rack.

Prepare the Glaze

1. Melt the Chocolate:
   • In a heatproof bowl, melt the dark chocolate, butter, and oil together, stirring until smooth.

Assemble the Cake

1. Layer the Cake:
   • Place the first baked layer into a baking tray.
   • Spread an even layer of the filling over it.
   • Repeat the layering process, finishing with a dough layer on top.
2. Add the Glaze:
   • Pour the hot chocolate glaze over the top of the cake, spreading evenly.
3. Chill the Cake:
   • Refrigerate the assembled cake overnight to set.

Serve

1. Cut and Serve:
   • The next day, cut the cake into small rectangles and serve.