Add the remaining 2 teaspoons oil to the wok. Add ginger and stir-fry until fragrant, 10 to 20 seconds. Add onion; stir-fry for 30 seconds. Add bell pepper and broccoli; stir-fry for 30 seconds. Pour in the remaining 1/4 cup broth, cover and cook until the vegetables are crisp-tender, 2 to 4 minutes. Push the vegetables to the sides. Stir the sauce mixture and add it to the wok. Cook, stirring, until the sauce becomes thick and translucent. Stir the vegetables into the sauce and return the beef to the wok; toss to coat. Serve immediately.