Step 1: Preheat your oven to 425°F (220°C).
Step 2: Grease your ramekins with butter and dust with flour.
Step 3: In a double boiler or microwave-safe bowl, melt the chocolate and butter together.
Step 4: In a separate bowl, whisk together the light brown sugar and confectioners' sugar.
Step 5: Add the egg, egg yolk, and vanilla extract to the sugar mixture and whisk until smooth.
Step 6: Gradually mix in the melted chocolate and butter mixture.
Step 7: Sift in the flour and salt, gently folding until no flour streaks remain.
Step 8: Divide the batter evenly between the ramekins, filling them 3/4 full.
Step 9: Bake for about 12-14 minutes until the edges are firm but the center jiggles slightly.
Step 10: Let the cakes sit for 1 minute before inverting them onto plates and serving immediately.