Heat the olive oil in a large soup pot or Dutch oven over medium-high heat. Add the chopped onion and cook until it's soft and translucent, about 2 to 3 minutes.

Stir in the ground beef, breaking it up as it cooks. Continue cooking for approximately 5 to 7 minutes until browned.

Once the beef is cooked through, add the minced garlic and sauté for 1 minute. Next, stir in the tomato paste, salt, and black pepper.

Gradually pour in the broth, scraping the bottom of the pot to release any flavorful bits. Add the diced tomatoes, crushed tomatoes, chopped carrots, sliced cabbage, and rice.

Bring the mixture to a boil, then cover and reduce the heat to medium-low, allowing it to simmer gently. Cook for about 20 minutes until the rice is tender and the vegetables are cooked through.

Stir in the Worcestershire sauce and optional brown sugar. If the soup has thickened too much, add a cup of water to reach your desired consistency. Taste and adjust seasoning with more salt and pepper if necessary.

Serve the soup in bowls and top with a sprinkle of chopped parsley.