Begin by preheating your oven to 375°F (190°C). Grease your 9-inch round cake pan with butter or cooking spray, then line the bottom with parchment paper for easy removal later.
In a double boiler or a heatproof bowl set over a pot of simmering water, combine the chopped bittersweet chocolate and cubed unsalted butter. Stir gently until both are completely melted and smooth. Remove from heat and let it cool slightly.
In a large mixing bowl, use an electric mixer to beat the chilled eggs on high speed until they are thick and tripled in volume, which should take about 5-7 minutes.
Once the chocolate mixture has cooled slightly, add the brewed coffee, salt, and vanilla extract. Stir until well combined. Gently fold about one-third of the whipped eggs into the chocolate mixture to lighten it. Then, carefully fold in the remaining eggs until no streaks remain.
Pour the batter into your prepared cake pan, smoothing the top with a spatula. Bake for 25-30 minutes, or until the edges are set and the center is slightly soft and jiggly.
Allow the cake to cool in the pan for about 10 minutes. Run a knife around the edges to loosen it, then invert the cake onto a plate. Peel off the parchment paper, and let it cool completely. Dust with powdered sugar before serving for an elegant touch.
