Preheat your oven to 325°F (160°C). Grease a 9-inch springform pan lightly and line the bottom with a circle of parchment paper.

Melt the chopped chocolate and butter together in a heatproof bowl set over a pot of simmering water (double boiler method), stirring until smooth. Remove from heat and let cool slightly.

In a large mixing bowl, whisk the egg yolks with 1/2 cup of the sugar, espresso powder, and vanilla extract until the mixture is pale and slightly thickened. Stir the cooled chocolate mixture into the yolks until combined.

In a separate clean, dry bowl, beat the egg whites and salt with an electric mixer until soft peaks form. Gradually sprinkle in the remaining 1/4 cup sugar and continue beating until stiff, glossy peaks form.

Gently fold one-third of the whipped egg whites into the chocolate mixture to lighten it. Then, very carefully fold in the remaining egg whites just until no white streaks remain, being careful not to deflate the batter.

Pour the batter into the prepared pan and smooth the top. Bake for 35 to 40 minutes, until the cake has puffed up and a toothpick inserted into the center comes out with moist crumbs attached (not wet batter).

Let the cake cool completely in the pan on a wire rack. The cake will deflate in the center and crack slightly as it cools, which is characteristic of this style. Remove the pan sides and dust generously with cocoa powder before serving.