In a small bowl, combine the beef broth, cornstarch, and mustard, and stir until cornstarch is dissolved. Set aside.
Cut the broccoli and cauliflower into bite-size pieces. In a large nonstick skillet or wok, warm the oil over medium-high heat until very hot but not smoking. Add the broccoli, cauliflower, onion, and garlic, and stir-fry until the vegetables are crisp-tender and onion is brown, 4 to 5 minutes. Be careful not to burn the garlic.
Stir the cornstarch mixture again and pour it into the wok. Stir in the beef, peanuts, red pepper flakes, and black pepper, and stir-fry until the sauce thickens and beef is heated through, 2 to 3 minutes. If necessary, reduce the heat to keep the sauce from evaporating. Makes 4 servings. Enjoy!