Heat the olive oil in a large pot over medium heat. Add the diced onion and sauté until translucent, about 3 minutes. Add minced garlic and cook for another minute until fragrant.
Add the ground beef and cook until browned all over, breaking it up with a spoon as it cooks.
Stir in the diced bell peppers, petite diced tomatoes, tomato sauce, water, beef broth, dried parsley, basil, oregano, black pepper, bay leaf, red pepper flakes, and rice. Mix well.
Bring to a gentle boil, then reduce heat to low and cover. Let it simmer for about 30 minutes.
Remove from heat, discard the bay leaf, and ladle into bowls to serve.