Heat oil in a skillet over medium-high heat. Brown beef for 7 minutes until no pink remains; drain excess fat.
Add onion; cook 4 minutes. Stir in garlic for 30 seconds.
Transfer to a 6-quart slow cooker; add peppers, both tomatoes, broth, Worcestershire, oregano, and salt.
Cover; cook on low for 5 1/2 to 6 hours until peppers are tender but intact.
Bring rice and water to a boil in a saucepan. Cover; cook over low heat about 15 minutes until tender.
Fold rice into soup just before serving to keep grains distinct.