Heat the oil in a skillet over medium-high heat and brown the beef until no pink remains, 7 minutes; drain excess fat.
Add the onion and cook for 4 minutes, then stir in the garlic for 30 seconds.
Transfer the beef mixture to a 6-quart slow cooker and add the bell peppers, both tomatoes, broth, Worcestershire, oregano and salt.
Cover and cook on low until the peppers are tender but still recognizable, 5 1/2 to 6 hours.
Combine the rice and water in a saucepan, bring to a boil, cover and cook over low heat until tender, about 15 minutes.
Fold the cooked rice into the soup just before serving so the grains stay distinct.