Season the beef with the salt and pepper and brown it in two batches in the oil, 4 to 5 minutes per batch.
Transfer the beef to a 6-quart slow cooker and add the onion and garlic.
Whisk the broth, soy sauce, brown sugar and tomato paste and pour the mixture into the cooker.
Cover and cook on low until the beef is tender, 6 1/2 to 7 hours.
Stir in both bell peppers and cook on high until crisp-tender, 25 to 30 minutes.
Whisk the cornstarch with the cold water, stir it into the sauce and cook until glossy, about 8 minutes.
Combine the rice and water in a saucepan, bring to a boil, cover and cook over low heat until tender, 15 to 18 minutes.
Serve the pepper steak and sauce over the steamed rice.