Preheat your oven to 350¬ºF and lightly grease or butter a 22 centimeter springform pan, line the bottom with a round of parchment paper, and dust the sides of the pan with flour, tapping out any excess.
In a large glass or metal bowl or the bowl of your stand mixer, whip the egg whites and salt together until soft peaks form. With the mixer running, gently sprinkle in one tablespoon of sugar and continue to whip until stiff peaks form. Transfer the whipped egg whites to a separate bowl and set aside.
In the bowl you whipped your egg whites in, combine the remaining 2/3 cup of sugar and butter. Beat on high speed for two minutes until light and fluffy then beat in the egg yolks. Scrape down the bowl and continue to beat for an additional minute or two until the mixture is well combined and light in colour. Add the melted chocolate to the butter mixture and begin to slowly combine the mixture. In a small bowl, combine the espresso powder, rum, and almond extract then, with the machine running, drizzle it into the chocolate and butter mixture. Beat well to combine.
Using a spatula, fold approximately a third of the whipped egg whites into the chocolate and butter mixture. Gently fold in half of the flour followed by another third of the whites. Fold in the remaining flour followed by the final dose of whipped egg whites just until combined.
Gently pour the batter into your prepared springform pan, spread it into an even layer, and bake in your preheated oven for 25 minutes or until the edges of the cake are set and dull and the centre still looks a little under cooked. Allow the cake to cool in the pan for 20 minutes then run a knife around the edge of the pan, release the sides of the springform, and flip the cake out onto a cooling rack. Remove the parchment paper and allow the cake to cool completely.
While the cake cools, make the ganache glaze by melting together the semisweet chocolate and rum over a double boiler or in the microwave. Allow it to cool slightly then, using a spoon, beat in the butter, one tablespoon at a time. Finally, beat in the vanilla and salt and allow the glaze to cool to a thin spreadable consistency, giving it a stir every once in a while.
When the cake has cooled and the glaze is spreadable, pour it over the cake and spread it around making sure to coat the top and sides. Finish the cake by scattering sliced almonds over the top or up the sides of the cake.