1. Place sugar in a 2-quart heavy saucepan. Cook over medium heat 3 to 4 minutes or until a deep amber color. Remove pan from heat; add milk, butter, and salt (mixture will bubble vigorously). Return pan to heat. Cook, stirring constantly, until blended and smooth. Remove from heat; cool 3 minutes (do not allow caramel to harden). Reserve 2 tablespoons caramel sauce.
2. Place ice cream in a blender. Remove center piece of blender lid; secure blender lid on blender. With blender on, slowly pour caramel sauce into ice cream; process until smooth.
3. Pour ice cream mixture into 6 tall glasses. Drizzle reserved caramel sauce over milk shakes.