5. After 15 to 20 minutes, when the mixture begins to thicken and coats the back of the spoon, add the chocolate. Continue stirring for about 2 to 4 minutes, or until the pudding is smooth and thickened. Remove from the heat and stir in the vanilla. Transfer to a small bowl and cover, gently pressing a layer of plastic wrap against the surface before refrigerating (this will prevent a skin from forming). Refrigerate for at least 30 minutes and up to 3 days.