Preheat oven to 400 degrees F. Place rack in center of oven. Butter four - 6 to 8 ounce (180-240 ml) molds, ramekins, or custard cups and dust the insides with granulated white sugar. Place the prepared molds on a baking sheet and set aside while you make the cake batter.
In a heatproof bowl, placed over a saucepan of simmering water, melt the butter and chocolate. Remove from heat and set aside while you beat the egg yolks.
In the bowl of your electric mixer, or with a hand mixer, beat the egg yolks and 1/3 cup (65 grams) sugar until thick, pale, and fluffy. (When you slowly raise the beaters the batter will fall back into the bowl in slow ribbons.) Beat in the vanilla extract and then fold in the melted chocolate mixture.
In another clean bowl whip the egg whites until frothy. Add the cream of tartar and continue to whip until soft peaks form. Gradually add the 1 tablespoon of granulated white sugar and whip just until stiff peaks form. With a rubber spatula or wire whisk gently fold the beaten whites into the chocolate mixture, just until incorporated. Do not over mix or the batter will deflate.
Divide the batter between the prepared molds. Bake for 10 to 15 minutes or until the outside edges of the cakes are set but the middle still looks a little wet and wobbly.
Immediately remove from oven and let them rest for a minute or two.