Heat 2-1/2 cups of milk until bubbles appear around the edges of the pan. In the meantime, sift the brown sugar, cornstarch and salt together into a bowl. Add the remaining 1/2 cup milk and mix ingredients until smooth. Add the heated milk, blend thoroughly with a whisk and return the mixture to the pan. Cook over low-medium heat, stirring frequently, until the pudding is smooth and thick (2-3 minutes). Let cool slightly. Stir in the butter and vanilla extract. Spoon into dessert dishes. Chill and serve.