Preheat the oven:Preheat your oven to 350°F (175°C). Butter and flour an 8-inch round cake pan and line it with parchment paper for easy removal.
Melt the chocolate:Place the chopped chocolate and coffee or rum in a heatproof bowl set over simmering water. Stir until melted and smooth. Set aside to cool.
Prepare the cake batter:In a stand mixer fitted with a paddle attachment, cream together the butter and 2/3 cup sugar until pale and creamy. Add the egg yolks one at a time, beating until smooth. Stir in the cooled melted chocolate, almond extract, and almond flour.
Whip the egg whites:In a separate bowl, beat the egg whites and salt on high speed until foamy. Gradually add the remaining sugar (1 tablespoon) and continue beating until stiff peaks form.
Fold the ingredients together:Gently fold one-quarter of the whipped egg whites into the batter to loosen it. Then, fold in the remaining egg whites in three additions, alternating with the sifted cake flour. Be careful not to deflate the batter.
Bake the cake:Pour the batter into the prepared cake pan and smooth the top. Bake for 25-30 minutes, or until the edges are set, and the center is slightly jiggly when gently bumped.
Cool the cake:Allow the cake to cool in the pan for 10 minutes before running a knife around the edges. Turn the cake out onto a wire rack and let it cool completely.
Prepare the icing:In a heatproof bowl over simmering water, melt the chopped chocolate and coffee or rum. Stir until smooth. Gradually add the butter, one tablespoon at a time, whisking until fully incorporated. Let the icing cool to a spreadable consistency.
Frost the cake:Spread the cooled icing over the cake and garnish with slivered almonds.