Step 1Heat the oven to 350 degrees. Grease and flour an 8-inch round cake pan.
Step 2Melt the chocolate in the top of a double boiler set over, but not touching, simmering water. Add the butter and stir. When the mixture is thoroughly melted, add the ground almonds, pouring in a thin stream. Stir to blend. Remove from the heat and set aside.
Step 3Place the eggs and yolks in a mixing bowl with 3/4 cup of the sugar and the cocoa powder. Whisk until blended, then stir into the almond-chocolate mixture. Set aside.
Step 4Place the egg whites in the bowl of an electric mixer. Add the salt and beat until they hold stiff peaks, about 4 minutes. Add the remaining 1 tablespoon sugar and the vanilla and beat to combine. Gently fold the beaten whites into the chocolate mixture.
Step 5Transfer the batter to the pan. Bake until the tip of a knife inserted in the center comes out clean, 25 to 28 minutes.
Step 6Prepare a large plate with a clean dish towel on top. Remove the cake from the oven and unmold onto the towel-covered plate. Let cool. Transfer to a serving platter and dust with cocoa, if desired.