In a large pot, heat olive oil over medium heat. Add diced onions and cook until soft and translucent.
Add ground beef and cook until browned, breaking it apart with a spoon. Drain any excess fat if needed.
Stir in minced garlic and diced bell peppers. Cook for about 5 minutes until the peppers start to soften.
Stir in diced tomatoes, tomato sauce, beef broth, oregano, and basil. Mix well to combine all ingredients.
Bring the soup to a gentle boil, then reduce heat and let it simmer uncovered for 20 minutes to develop flavor.
Stir in the cooked rice and simmer for an additional 5 minutes.
Taste and adjust salt and pepper. Serve hot, garnished with fresh herbs or shredded cheese if desired.