Mix the egg whites with a pinch of salt, then add the sugar and continue to mix until you get a meringue.
Separately mix the yolks with melted and cooled butter, then add them over the meringue.
At the end, add the flour, sprinkling it lightly and incorporating it into the dough with a wooden spoon, in movements from top to bottom, so that the dough will remain aerated.
From this composition we bake 3 sheets in a row, in a large tray on the stove, lined with baking paper.
(I baked each sheet for about 15 minutes, over medium heat, on the furthest part of the fire.)
When they are ripe, take the sheets out of the tray and portion them into 3 equal pieces. In this way we obtain 9 sheets for the cake.
In a saucepan mix the eggs with the sugar and the rum-flavored sugar and put on the steam bath, stirring until the sugar melts.
Remove from the heat and mix the composition until it forms blisters.
Separately, break pieces of dark chocolate that we will melt, along with two tablespoons of butter, in the microwave (or on the fire). When the chocolate is melted, add the cocoa, mix and let it cool slightly, then add it over the egg composition, mixing to blend.
Mix the butter previously kept at room temperature. When it becomes frothy, we pour, little by little, from the chocolate composition, mixing continuously to obtain a fine cream, uniform in texture.
Assemble the cake alternating the sheets with suitable layers of cream, until we cover the 8th sheet with cream.
We keep a countertop sheet to cover it with caramel. For this, melt 150 g of sugar, being careful not to burn it. We will slice the preserved sheet into equal strips, 1-2 fingers wide. When the caramel is ready (the sugar is completely melted), pour it evenly over the strips, taking care to separate them until the caramel has not hardened. For this we will use a knife passed through butter.
Cover the cake in cream, and place the caramel strips on top.
After being cold for 2-3 hours, the cake is ready to serve.