Cook carrots in a small amount of boiling salted water 10 minutes or until crisp-ender; drain and set aside.
Combine vinegar and broth in a saucepan; bring to a boil. Reduce heat; simmer 2 minutes.
Combine sugar and flour; stir well, and sprinkle in a 10-inch cast-iron skillet. Place over medium heat, stirring constantly with a wooden spoon until sugar melts and becomes a light golden brown. Gradually add vinegar-broth mixture, stirring to make a smooth syrup. Add carrots; cook over medium heat 15 minutes or until carrots are tender.