Stir soy sauce, cornstarch, garlic, and crushed red pepper together in a large, non-metal bowl until well combined. Add steak and toss to coat. Cover the bowl and refrigerate for 20 minutes.

Heat oil in a wok or large skillet over high heat. Stir-fry beef in hot oil until no longer pink, about 5 minutes. Add broccoli, onions, and water chestnuts; cook and stir for 2 minutes. Pour in broth and bring to a boil. Stir in peanuts; cook for 1 minute and serve hot.