Combine chocolate, milk and sugar in heavy saucepan.
Heat chocolate, milk and sugar in a heavy saucepan, stirring constantly until chocolate is melted and the mixture comes to a boil.
Remove from heat and add butter and vanilla.
Stir until butter is melted and incorporated into the chocolate sauce.
Let cool for 5 minutes to thicken before serving.
May be stored in the refrigerator for up to 2 weeks if it lasts that long!