Mix broth, soy sauce, vinegar, brown sugar, garlic, and ginger in a 4-quart slow cooker. Add steak strips, separating in sauce.
Cover; cook on low about 6 hours until 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; cook 40 to 45 minutes. Rest covered 10 minutes.
Mix cornstarch with 2 tablespoons cold water; stir into cooker. Add broccoli; cover and cook on high 20 to 30 minutes until florets are tender and sauce lightly coats beef.
Stir in sesame oil; rest 3 minutes.
Divide rice, beef, and broccoli among 4 bowls.