Preheat oven to 325 degrees F. Line the bottom of a 9-inch springform pan that is at least 3 inches high with parchment paper. Spray the bottom parchment and inside of the pan with cooking spray; set aside.
Melt the chocolate and butter together. You can either do this in a double boiler on the stove by: placing the chocolate and butter in a large heatproof bowl, set over a boil of gently simmering water, and stirring until melted and smooth. Or you can do this in the microwave by: heating the chocolate and butter in a microwave-safe bowl in 30-second intervals, stirring in between, until the chocolate and butter are melted and smooth.
Let melted chocolate cool for 5 minutes then whisk in egg yolks, vanilla and baking powder; set aside.
In a stand mixer fitted with the whisk attachment, beat the egg whites, cream of tartar and salt at medium speed until frothy, about 30 seconds. Add ¼ cup brown sugar and beat to combine, then add the remaining brown sugar and beat at high speed until soft peaks form, scraping down the sides halfway through. (Soft peaks means when you remove the whisk, a peak is just starting to hold and then droop after a second.)
Using a rubber spatula, fold the beaten egg whites into the chocolate mixture in thirds until no white streaks remain. Transfer the batter to the prepared springform pan, tap on the counter a few times, then smooth the top with a spatula.
Bake at 325 degrees F until the cake has risen in the center and the edges are set (a toothpick will NOT come out clean), 16-20 minutes. Transfer the pan to a wire rack to cool completely, about 1 hour. The cake will collapse slightly as it cools. You can begin making the mousse 45 minutes after cooling.
Once the cake has cooled, temporarily remove the springform pan. Snuggly encircle the cake with parchment paper that reaches about 1 inch above the edge of the springform (you can tape the parchment to itself.) Re-place the springform pan and re-clasp. Set aside.