Preheat oven to 450°F. Grease four (6-oz) ramekins really well with either cooking spray or butter. Place on a small baking sheet.
Add butter and chocolate to a small saucepan and set over your lowest heat setting. Stir frequently until the mixture is completely melted and smooth; remove from heat.
Beat the eggs, egg yolks, granulated sugar, vanilla, and salt in a large bowl with a hand mixer on high speed 2 to 3 minutes or until thickened and pale.
Slowly stream the chocolate mixture into the egg mixture and fold until no streaks remain. If you can stream the chocolate into the eggs while you're also mixing, even better, because we don't want the eggs to curdle!
Slowly and very gently fold in the flour, just until no streaks remain.
Spoon the batter into your prepared ramekins and bake for 9 to 10 minutes, just until the tops of the cakes are set. This is a time you'll want to watch the cakes very closely. If you bake them too long you may not end up with those perfectly gooey centers!
Remove the pan from the oven and let the cakes cool for 1 minute. Working with one cake at a time, flip the ramekin over, let it stand for about 10 seconds, and then lift the ramekin from the cake. Repeat with the remaining cakes.
Serve the cakes immediately with ice cream and powdered sugar, if you'd like!