Heat the oil in a large skillet over medium-high heat; add steak strips and stir-fry until browned; transfer to a slow cooker.
Add onion, garlic, bok choy, broth, soy sauce, and gingerroot. Cover and cook on LOW for 6 to 8 hours.
In a small bowl, combine cornstarch and water until smooth. Raise slow cooker heat setting to HIGH and stir in cornstarch mixture.
Add broccoli and continue to cook until sauce is thickened and broccoli is heated through.