Brown onions, garlic, salt, pepper, and ground beef in a large and deep skillet or pot. Drain fat and add remaining ingredients of chicken stock, chopped smoked sausage, tomato sauce, brown sugar, oregano, and thyme, cabbage.
Bring mixture to a low boil. Lower temperature to a low-medium heat and cover. Cook for 40-60 minutes or until cabbage is tender. This may take a bit longer depending on how much cabbage is in your pot.
For a slow cooker: Brown onions, garlic, salt, pepper, and ground beef in a skillet. Drain fat and toss in the slow cooker. Add remaining ingredients and cook on low for 6 hours.
For a pressure cooker: Brown onions, garlic, salt, pepper, and ground beef in a skillet. Drain fat. Set all in a pressure cooker and set on medium pressure for 10 minutes.