Combine brown sugar, syrup, vinegar and salt in a large, heavy saucepan over low heat. Stir until the sugar dissolves, cover with a lid briefly to get any sugar crystals off the sides of the pan. Bring to a boil, stirring constantly.
Add milk in a thin stream, stirring constantly. Cook to firm ball stage (248°F / 120°C), or until a small amount of mixture is dropped into cold water and forms a ball that holds until pressed. Remove from heat.
Pour mixture onto a buttered marble slab or similar surface. As soon as outside edges cool enough to touch, take a small portion of the candy and start stretching or pulling. Use only the tips of your (greased) fingers. Pull until taffy becomes light in color and is no longer sticky.
Twist each pulled strip slightly and place on waxed paper. When all the candy is pulled, cut each piece into about 1-inch pieces. Wrap each piece in waxed paper and twist ends. Store in covered container at room temperature.