Preheat the oven to 325° F. Prep the cake pans by brushing them with melted butter, lining with parchment paper cut to size, and brushing the parchment paper with butter as well. Dust with unsweetened chocolate powder. Set aside.
Bring some water in a wide pan on the stove to a boil. Turn off the heat. Place the butter and chocolate in a small bowl, cover with plastic wrap, and place the bowl in the hot water so that it floats without touching the bottom of the pan. After about 10 minutes, remove the bowl and the plastic wrap, and stir gently with a spatula. Return to the hot water for about 5 more minutes and stir gently with a spatula. Keep doing this until the chocolate and butter are completely melted and combined. Set aside to cool slightly (As you’re doing this, be careful not to get any drops of water in the chocolate mixture.)
While the chocolate is melting, place the egg yolks and sugar together in the bowl of an electric mixer fitted with a paddle attachment. Beat on high until the mixture becomes slightly thickened and turns a pale yellow (about 4 minutes). Scrape down the bowl, add the salt, vanilla extract and rum. Mix on high for another 2 minutes.
In a separate bowl, with an electric mixer, whip the egg whites until stiff but not dry. Set aside.
Using a spatula or with the mixer on its lowest setting, fold the chocolate mixture into the egg yolk mixture. Using a spatula, fold the sifted flour in thirds into the chocolate/yolk mixture. Only fold long enough to integrate the flour into the wet mixture, no longer. Fold in the whipped egg whites in thirds. Always be careful not to overfold. There is no chemical leavener in the recipe and is dependent upon the air that’s been whipped in as the only leavener for this cake.
Divide the batter between the baking pans and bake on the middle rack. I baked this in 6″ baking pans, which took 18-20 minutes to bake. For an 8″ baking pan it may take 25 minutes. Cake is ready when it’s firm to the touch and a toothpick in the middle comes out clean.
Remove from the oven, and leave the cake in the pans for 15 minutes on a cooling rack. To remove the cake from the pan, run a sharp knife around the edge, and flip it over onto the cooling rack. Keep the buttered parchment paper on the cake until you’re ready to frost and assemble. Let the cake completely cool before applying the filling and frosting.