Stir broth, soy sauce, vinegar, brown sugar, garlic and ginger in a 4-quart slow cooker. Add steak strips and separate them in the sauce.
Cover and cook on low for about 6 hours until the beef is tender and reaches at least 145°F.
During the final hour, bring rice and 1 1/2 cups water to a boil in a covered saucepan, reduce to low and cook for 40 to 45 minutes, then rest covered for 10 minutes.
Stir cornstarch mixed with 2 tablespoons cold water into the cooker. Add broccoli, cover and switch to high for 20 to 30 minutes until florets are tender and sauce lightly coats the beef.
Stir in sesame oil and let the finished mixture stand for 3 minutes.
Divide rice, beef and broccoli among 4 bowls.