Preheat an oven, then butter a 9-inch springform pan on all sides. Line with enough parchment paper to hang over the sides generously (this will make it easier to remove later).
Place chocolate and butter in a large microwave-safe bowl, then heat on high in 30 second increments, stirring after each addition, until both the butter and chocolate are completely melted. Let cool slightly.
Place egg whites in the bowl of a stand mixer, then whisk until soft peaks form. With the mixer on low, slowly pour in sugar, then continue whisking until the egg whites are glossy and have stiff peaks.
To the cooled chocolate mixture (it must be cool or you’ll scramble the eggs!), whisk in the remaining sugar until smooth. Next, whisk in egg yolks, vanilla extract, espresso powder, and a pinch of Kosher salt.
Gently fold the egg white mixture into the chocolate mixture in 3 additions, being sure that the egg whites are fully incorporated before adding more. Try hard not to deflate the egg whites as you fold them into the batter.
Pour the flourless cake batter into the prepared pan, then smooth into a flat layer with an offset spatula. Bake until the cake has puffed up and a cake tester inserted into the center comes out clean.
The cake can be enjoyed warm, room temperature, or cold. I prefer it warm, but it will slice more neatly if allowed to cool (you can then reheat individual slices in an oven or microwave). Dust with cocoa powder and serve with lightly whipped cream (or creme fraiche) and berries.