Heat olive oil in a large Dutch oven or heavy-bottomed stockpot over medium-high heat. Add the ground beef and cook, breaking it into small crumbles, for 6–8 minutes until deeply browned. Do not rush this step — the browning builds the soup's flavor foundation. Drain any excess fat, leaving about 1 tablespoon in the pot.

Add the diced onion to the pot with the browned beef. Cook over medium heat, stirring occasionally, for 4–5 minutes until the onion is softened and translucent. Add the minced garlic and cook for another 60 seconds until fragrant.

Stir in the smoked paprika, dried oregano, dried thyme, salt, and black pepper. Cook for 30 seconds, stirring constantly, to bloom the spices.

Add the crushed tomatoes, tomato sauce, beef broth, water, and Worcestershire sauce. Stir to combine, scraping up any browned bits from the bottom of the pot.

Add the chopped cabbage and stir to submerge it as much as possible in the liquid. Bring the soup to a boil over high heat, then reduce to a steady simmer. Cover and cook for 10 minutes until the cabbage begins to soften.

Stir in the uncooked long-grain white rice. Re-cover the pot and continue simmering for 18–20 minutes, stirring occasionally, until the rice is fully cooked and tender and the cabbage is soft.

Taste and adjust seasoning with additional salt and pepper as needed. If the soup is thicker than you prefer, stir in an additional splash of beef broth or water to reach your desired consistency.

Ladle into bowls and garnish with fresh chopped parsley or dill. Serve with a dollop of sour cream if desired.