To begin, heat oven to 325 degrees. Butter interior of pan.
Melt butter, chocolate, and espresso powder in large heatproof bowl set over saucepan filled with 1 inch of barely simmering water. Stir occasionally until smooth. Remove from heat and cool for about five minutes. Get your egg yolks and vanilla, and whisk them in until incorporated.
With a hand held mixer or stand mixer, beat egg whites and salt at medium speed until frothy, about 30 seconds. Add half of brown sugar and beat until combined, about 15 seconds. Add remaining brown sugar and beat at high speed until soft peaks form when whisk is lifted, about 1 minute longer, scraping down sides halfway through.
With a whisk, fold one-third of beaten egg whites into chocolate mixture to lighten. Now get a rubber spatula and fold in remaining egg whites until no white streaks remain.
Gently pour batter into springform pan.
Bake until cake has risen, is firm around edges, and center has just set but is still soft,13 to 18 minutes.
Transfer cake to wire rack to cool completely, about 1 hour. (Cake will collapse as it cools.)
Do not remove cake from pan.