Butter a 9-inch springform pan. Line with baking parchment and set aside.
Preheat oven to 350°F and place a rack in the center of the oven.
Place the chocolate and butter in a microwave (or over simmering water) and heat, in 30-second increments, until the butter has melted and the chocolate has begun to melt.
Place the brown sugar and water in a saucepan over medium heat and bring to a boil, stirring very often.
Pour boiling sugar over chocolate mixture and stir until completely melted and smooth.
Add egg yolks, one at a time, incorporating completely before adding the next. Set aside until cool.
In the bowl of a stand mixer fitted with the whisk attachment, whip egg whites and salt until stiff but glossy peaks form.
In three additions, fold egg whites into chocolate mixture.
Pour two-thirds of the batter into the prepared pan, and bake 45-55 minutes, or until a skewer inserted into the center comes out mostly clean.
Remove from oven and let cool completely on a baking rack.
If needed, use a spatula to push down the cake, then pour remaining batter over the top and smooth.
Bake an additional 30 minutes, or until a skewer inserted comes out with clumps of cake clinging to it.
Cool completely before removing from the springform pan.