In a large 10-inch skillet cook ground beef and onion over medium heat, for about 5 minutes. When beef is cooked and onion is translucent, drain excess liquid. Add garlic to the skillet and sauté for 30 seconds more.
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.
