Preheat oven to 350°F. Grease a 9-inch pan (preferably springform), and line the bottom with parchment paper. Butter the paper, then lightly dust flour along the sides of the pan. Tap out the excess flour. Set aside.
Melt the chocolate in a bowl set over a pan of very hot, but not simmering, water, stirring occasionally. Once completely melted, remove from the heat and let cool, stirring often.
In a large bowl, beat the egg whites and superfine sugar with a handheld mixer on high speed just until soft, shiny peaks form. Set aside.
In a small bowl, sift together the all-purpose flour, almond flour, and salt. Set aside.
Beat the butter in the bowl of a stand mixer on medium-high until smooth. Reduce the speed to low and beat in the confectioners sugar. Return the speed to medium-high and continue beating until light and fluffy, about 2 minutes. Add the egg yolks, one at a time, and beat until mixture is fluffy again, scraping down the sides of the bowl periodically. Beat in the chocolate and vanilla, then gradually add the flour mixture.
Beat about one-fourth of the beaten whites into the chocolate mixture. Using a spatula, gently fold in the remaining whites. No white streaks should remain.
Spread evenly in the pan and smooth the top. Bake on the center rack until a toothpick inserted in the center comes out clean or almost clean, about 35-45 minutes.
Let cake cool in the pan on a wire rack for 10 minutes, then remove sides of the pan (if using a springform pan) and invert the cake onto the rack. Remove the paper and reinvert the cake onto another rack right side up. Allow to cool completely.