Warm the vegetable oil in a large pot over medium-high heat. Add the ground beef, season with salt and pepper, and cook until it turns brown and is no longer pink.
Add the finely diced onion and minced garlic to the pot and cook, stirring often, until the onions soften and become 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.
Reduce the heat to low and let the soup gently simmer for about 25 minutes, or until the rice is fully cooked and tender.
Take out the bay leaf, sprinkle the fresh chopped parsley on top, and serve the soup hot for a comforting meal.