Melt 1/4 a stick of butter in a small saucepan over low heat. Paint the inside of 6 ramekins or aluminum souffle cups with butter. Coat the inside of each ramekin with granulated sugar. Reserve.
Put the remaining stick of butter and chocolate chips in a large mixing bowl. Set the bowl on a saucepan filled with about 1-inch of boiling water. Be sure that the bowl is not touching the water. Gently stir the butter and the chocolate together until melted and the mixture is smooth. Turn off the heat and reserve.
Combine the eggs, yolks, sugar and vanilla in the bowl of a stand mixer. (This can also be done with a hand beater.) Beat the egg mixture until it doubles in size, and gets very thick and very pale.
Gently whisk the melted chocolate and butter into the egg mixture. Remove the bowl from the mixer and gently stir in the flour. Pour the batter into the prepared ramekins. Arrange the ramekins on a baking sheet and bake in the preheated oven for 14 to 15 minutes. Remove the cakes from the oven and let rest for 3 to 4 minutes.
Remove the cakes from the ramekins, and arrange them on individual serving plates. Dust with powdered sugar and garnish with crushed candy cane.