Preheat oven to 350°F (175°C). Butter two 5- or 6-ounce ramekins. Dust with cocoa powder and shake out the excess.
Place chocolate and 2 tablespoons butter in a microwave-safe bowl. Heat at half-power in the microwave in 30-second increments until the butter has melted and the chocolate melts when stirred. Stir until smooth. Set aside to cool slightly.
Using an electric mixer on medium speed, beat the sugar, brown sugar, egg, vanilla, and salt until combined. Add the chocolate mixture and mix until smooth.
Divide the batter evenly between the prepared ramekins.
To make it easier to put the cakes in the oven and take them out, place them on a rimmed baking sheet. Bake 20 to 25 minutes or until cakes are set.
Serve warm in the ramekins. Garnish with whipped cream and chocolate shavings.