Brown the Meat: Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the ground beef, onion, and a pinch of salt. Cook until the meat is browned and the onion is soft (about 5–7 minutes). Drain any excess fat if necessary.
Add Aromatics: Add the minced garlic and cook for 1 minute until fragrant.
Build the Soup: Add the chopped cabbage, carrots, diced tomatoes, tomato sauce, beef broth, Worcestershire sauce, paprika, thyme, brown sugar, and bay leaf. Stir well to combine.
Simmer: Bring the pot to a boil, then reduce heat to medium-low. Cover and let simmer for about 15–20 minutes, or until the cabbage begins to soften significantly.
Add the Rice: Stir in the uncooked rice. Cover again and simmer for another 15–20 minutes, or until the rice is tender.
Finish: Remove the bay leaf. Taste the soup and season with additional salt and pepper as needed. If the soup is too thick, splash in a little extra broth or water.