Melt 2 tablespoons of the butter in a small saucepan over low heat. Paint the insides of 6 ramekins with the melted butter, then coat with granulated sugar.
Put the remaining stick of butter and the chocolate chips in a large mixing bowl. Set the bowl over a saucepan filled with about 1 inch of boiling water (make sure the bowl doesn't touch the water). Gently stir the butter and chocolate together until melted and smooth. Turn off the heat.
Combine the confectioners' sugar, vanilla, eggs and yolks in the bowl of a stand mixer fitted with the whisk attachment. Whip until doubled in size and very thick and pale. Gently whisk in the chocolate-butter mixture. Gently stir in the flour. Pour the batter into the prepared ramekins. Place the ramekins on a baking sheet and bake for 14 to 15 minutes. Let rest for 3 to 4 minutes.
Whip the cream in a bowl with an electric mixer until it holds soft peaks.
Remove the cakes from the ramekins and place them on individual serving plates. Dust with confectioners' sugar. Serve warm with whipped cream.