Add tomato sauce, diced tomatoes, beef broth, paprika, thyme, brown sugar, salt, and pepper to skillet and stir. Add chopped cabbage and toss gently. Bring mixture to a boil.
Cover skillet, reduce heat to medium-low and simmer for 15 minutes. Stir, recover, then simmer for 10 minutes longer, or until cabbage is tender.
Remove lid and add 3 tablespoons of tomato paste. Stir and simmer, uncovered, for 5-10 minutes, or until sauce reduces slightly. If you prefer a thicker sauce, add additional tomato paste and stir. Garnish with fresh parsley and serve over cooked rice.