Preheat oven to 350°F and grease the bottom and sides of a 9-inch springform pan with softened butter.

Either in a large microwave-safe bowl or a double broiler, melt the chocolate and butter together, whisking until smooth. In the microwave, heat for 1 minute, whisk, then heat again in 30-second intervals until completely melted. Alternatively, use a double broiler or place a heat-proof bowl over a small saucepan of boiling water so the bottom of the bowl does not touch the water. Heat over medium heat, stirring constantly, until smooth. Set aside to cool slightly.

Meanwhile, in the bowl of a stand mixer fitted with the whisk attachment, or a large mixing bowl with a hand mixer, whip the egg whites with the cream of tartar over medium-high speed. Once the egg whites start to foam, slowly pour in the granulated sugar while the mixer is running and continue mixing just until stiff glossy peaks form.

Whisk the brown sugar, vanilla, and salt into the melted chocolate, then whisk in the egg yolks. Sift the cocoa into the melted chocolate and whisk to combine.

Use a silicone spatula to fold in ⅓ of the egg whites, mixing well to loosen the batter. Then carefully fold in the remaining egg whites in three parts, folding just until there are no white streaks remaining.

Spoon the batter into the prepared springform pan, smoothing the top. Then bake for 30-35 minutes, until the top puffs and crackles, while the inside still looks underbaked. The top should be somewhat firm to the touch. Note: if you underbake the cake, the top won't develop a nice crust, but if you overbake, the inside won't be as soft and chewy. I recommend erring on the side of underbaking. As it bakes, the cake puffs up and then falls and crackles as it cools.