Unstuffed Sweet-and-Sour Cabbage

Place cabbage in a deep 12-inch heavy skillet with broth, 1 garlic clove (sliced), and a rounded 1/4 teaspoon salt. Bring to a simmer over medium heat, then cook, covered, turning cabbage occasionally, until very tender, about 45 minutes. (Add more broth or water if necessary.)

Meanwhile, cook onion and remaining garlic in oil in a heavy medium pot over medium heat, stirring occasionally, until golden, about 8 minutes. Increase heat to medium-high and stir in ground meats along with 1/2 teaspoon each of salt and pepper. Cook, stirring and breaking up lumps with a wooden spoon, until no longer pink, about 3 minutes.

Stir in tomatoes with their juice, cranberries, vinegar, and brown sugar and simmer, uncovered, stirring occasionally and breaking up tomatoes with spoon, until slightly thickened, about 20 minutes. Season with salt.

Pour sauce into skillet with cabbage and simmer, uncovered, 5 minutes. Serve sprinkled with parsley.