Heat oven to 375° F. Use 1 tablespoon of the butter to grease one 16-ounce or three 8-ounce ramekins. Coat the ramekins with the cocoa powder, tapping out the excess.
In a large bowl, over a pan of simmering water, melt the chocolate and remaining butter. Stir occasionally until smooth. Remove from heat and add the vanilla. Whisk in the yolks one at a time until smooth. Set aside.
In a clean bowl, beat the egg whites with the sugar, salt, and cream of tartar until stiff, glossy peaks form. Gently fold the egg white mixture into the chocolate. Spoon into the ramekins, about 3/4 full. (The recipe can be made to this point up to 1 day ahead. Cover with plastic wrap and refrigerate.)
Bake until puffed and set, 40 minutes for a 16-ounce soufflé, 15-20 minutes for two smaller ones. (If baked directly from the refrigerator, add 5 to 10 minutes.) Serve immediately.