Put the butter in a medium bowl and melt it in the microwave. Add the chocolate to the hot butter and stir until melted.
In a medium bowl, whisk together the egg, egg yolk, and sugar, and beat or whisk until light and thick, about 1 minute. Add flour, and vanilla and whisk to combine. Add the melted chocolate/butter mixture and whisk until combined.
Butter and lightly dust with cocoa powder two 6-ounce molds or ramekins (make sure not to miss any spots, or the cakes will stick). Tap out the excess cocoa powder. Divide the batter among the molds. (At this point you can refrigerate them for up to 3 hours; just bring them back to room temperature before baking.)
When you’re ready to bake, heat the oven to 425°F. Put the molds on a rimmed baking sheet and bake until the cakes have puffed up a bit, the tops are barely set and the cakes still jiggle slightly when shaken, 11 to 12 minutes (better underbaked than overbaked). Let sit for a couple minutes.
Put a plate on top of the ramekin and (with a potholder to protect your hand) carefully invert the cake onto the plate. Let it sit for 10 seconds, then lift up the ramekin. Serve immediately. My preference is a scoop of vanilla ice-cream on top!
