Preheat your oven to 425°F.
Grease very well the entire insides of 4 4-ounce oven-safe ramekins and set them in a casserole dish with at least 2-inch high sides, and set aside.
Melt the chocolate and 4 tablespoons butter together in a double boiler or a microwave-safe bowl, stirring frequently until just melted. Set aside.
In a large bowl, place the eggs, egg yolks, sugar, and vanilla, and whisk to combine.
Whisk vigorously until the mixture is very pale yellow in color and thickened in consistency.
Drizzle the chocolate and butter mixture into the large bowl with the thickened egg mixture, whisking constantly until combined.
Add the flour, cocoa powder, and salt, and whisk to combine well.
Pour the mixture carefully into the 4 prepared ramekins, filling each ¾ of the way full.
Place the casserole dish with the filled ramekins on the bottom rack of the preheated oven and fill the dish with cool tap water until the water reaches about halfway up the sides of the ramekins.
Bake until the tops of the cakes are set and are just beginning to pull away from the sides of the ramekins, about 15 minutes.
Remove the ramekins from the casserole dish and let them cool on a wire rack for about 10 minutes before turning each cake out onto a small plate and dusting with confectioners' sugar. Serve immediately.