Heat the olive oil in a large soup pot over medium-high heat. Add the ground beef, season with salt and pepper to taste, and cook until the beef is browned; 4 to 5 minutes. Add the onion and garlic; continue to cook for 2 minutes more.
To the ground beef, add the cabbage, carrots, broth, tomatoes, rice, bay leaf, thyme, and brown sugar. Season with salt and pepper to taste and stir.
Bring the soup to a boil and then reduce the heat to maintain a simmer. Cook for 20 minutes, or until the rice is tender. Remove and discard the bay leaf; sprinkle with fresh parsley and serve.