Sift cake flour, 1 tablespoon sugar, and 1/4 teaspoon salt into a bowl.
Whisk 4 eggs and 1/2 cup sugar together in a bowl. Beat on high speed using an electric mixer until pale yellow and tripled in volume. Mix in 1 tablespoon vanilla extract. Add the flour mixture in 3 batches, mixing batter until fully incorporated after each addition.
Place melted butter into a bowl; add 1/2 cup of the batter and mix until smooth. Recombine with the main batter; mix until smooth. Pour batter into a round 9-inch baking pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 25 to 27 minutes. Remove from the oven and cool in the pan. Leave the oven on.
Sift all-purpose flour and 1 teaspoon salt together in a bowl.
Place 1 cup butter and chocolate in top of a double boiler over simmering water. Stir frequently, scraping down the sides with a rubber spatula to avoid scorching, until chocolate is melted, about 5 minutes. Add 1 cup sugar; stir briefly. Pour mixture into a large bowl.
Beat the remaining 1 cup sugar and 4 eggs together in a bowl using an electric mixer until just combined. Stir half gently into the chocolate mixture. Beat the remaining sugar-egg mixture until pale and doubled in volume; fold into the chocolate mixture. Add sifted flour mixture; mix until no dry spots remain. Pour batter into a round 9-inch baking pan.
Bake brownie in the still-hot oven until a toothpick inserted into the center comes out mostly clean, 23 to 25 minutes. Let cool in the pan, at least 20 minutes.
Transfer brownie layer to a plate; coat the top with frosting. Set genoise on top; spread frosting over the entire cake.