Cook bacon slices in a Dutch oven until crisp. Remove bacon, and drain on paper towels, reserving 2 tablespoons drippings. Crumble bacon.
Cook carrot in hot bacon drippings in Dutch oven over medium-high heat, stirring occasionally, 5 minutes. Add onion, and cook, stirring occasionally, 5 minutes or until carrot and onion begin to caramelize. Add garlic; cook, stirring constantly, 30 seconds. Add balsamic vinegar, and cook 30 seconds. Add collards, crumbled bacon, broth, and remaining ingredients. Bring to a boil; cover, reduce heat, and simmer 1 hour or until collards are tender.