Brown the ground beef in a large soup pot over medium heat for 7 to 8 minutes, breaking it apart and draining excess grease.
Add onions, garlic, and bell peppers; sauté 5 to 6 minutes until the onions turn translucent and the peppers soften.
Pour in diced tomatoes and tomato sauce, then add oregano, basil, salt, and pepper. Stir and let the mixture gently bubble.
Add 4 cups beef broth, bring to a boil, then reduce heat and simmer covered for 30 minutes until the peppers are tender.
Stir in 1 cup cooked rice and simmer 5 more minutes; add extra broth ½ cup at a time if the soup thickens too much.
Taste and adjust seasoning, adding crushed red pepper for heat or a splash of tomato sauce for sweetness.
Ladle into bowls and top with shredded cheese, letting it melt into a creamy layer.