Preheat oven to 375°F and adjust the rack to the lower-middle position. Generously grease 4 - 6 oz. ramekins with butter and coat with sugar.
Separate the eggs into separate bowls while they are cold and then set the egg whites aside to come to room temperature.
In a medium saucepan, heat the milk and then stir in the butter until melted. Remove from heat and whisk in the chocolate until melted and smooth.
Whisk the vanilla extract, flour, 2 tablespoons of sugar, and salt in with the egg yolks. In a slow and steady stream, pour the chocolate mixture into the yolks while whisking constantly.
Use a hand-held or stand mixer to whip the egg whites with the cream of tartar until soft peaks form. Add in 2 tablespoons of sugar and continue to whip for another 30 seconds. Add in another 2 tablespoons of sugar and whip until glossy stiff peaks form.
Gently fold the egg whites into the chocolate base until smooth. Pour into the prepared ramekins and level off the top with a knife.
Bake in the preheated oven for 14-16 minutes until they have risen 1-2 inches and are only slightly wobbly in the center. Do not open the oven door while they bake.
Sprinkle the tops with powdered sugar and serve immediately.