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.