Heat the vegetable oil in a large pot over medium-high heat. Add the ground beef, season with salt and pepper, and cook until it is nicely browned.
Add the finely chopped onion and minced garlic to the pot and cook, stirring frequently, until the onion softens and becomes translucent.
Pour in the chopped cabbage, sliced carrots, tomato sauce, beef broth, uncooked rice, bay leaf, and brown sugar. Stir everything together until well combined.
Lower the heat to a gentle simmer and let the soup cook uncovered for about 25 minutes, or until the rice is fully cooked and tender.
Take out the bay leaf from the soup and sprinkle fresh chopped parsley on top just before serving for a burst of fresh flavor.