In a large pot over medium-high heat, cook bacon until crispy, about 6-8 minutes. Use a slotted spoon to remove bacon to a plate; reserve drippings in the pot.
Add ground beef to the pot and cook over medium-high heat, breaking up the meat with a wooden spoon, until meat is no longer pink, about 5 minutes. Add the onion and cook until softened, about 3-4 minutes. Add the garlic and cook, stirring constantly, for 1 more minute. Add the tomato paste and cook, stirring constantly, for 1 more minute.
Stir in the cabbage, beef broth, tomato sauce, tomatoes, brown sugar and bay leaf. Bring to a boil; reduce heat to low, and simmer until the cabbage is tender, about 15-20 minutes.
Stir in the rice, season with salt and pepper to taste, and simmer for about 5 more minutes. Remove from heat, discard bay leaf, and stir in parsley. Ladle into bowls and garnish each bowl with reserved bacon.