Melt 4 Tablespoons of butter and the chopped chocolate together in a double boiler or in a large heatproof bowl in the microwave. Microwave in 20 second increments, stirring after each until completely melted and combined. Slightly cool for 3-5 minutes.
Whisk egg yolks, vanilla extract, and salt into chocolate mixture. Set aside.
In a completely clean residue-free medium glass or metal mixing bowl, using a handheld mixer or stand mixer fitted with a whisk attachment, beat the egg whites and cream of tartar together on high speed until soft peaks form, about 2 minutes. With the mixer running on high speed, slowly add the sugar in 3 additions about 1 Tablespoon at a time, beating for 5 seconds before adding the next Tablespoon. After all 3 Tablespoons of sugar have been added, beat until stiff glossy peaks form, about 2 more minutes. Do not over-beat.
Slowly and gently fold the egg whites into the chocolate mixture. It’s best to do this in 3 separate additions, combining each addition completely before folding in more.
Refrigerate the batter for 5-10 minutes as you preheat the oven and prepare the ramekins. (No need to cover the batter unless you are refrigerating it for longer than 1 hour. Can be made up to 2 days in advance, see make ahead instructions below.)
Adjust the oven rack to the lower third position and preheat to 400°F (204°C).