Trim fat from beef.
Cut beef with grain into 2-inch strips.
Cut strips across grain into 1/8-inch slices.
(Beef is easier to slice if partially frozen.) Toss beef, 1 tablespoon oil, 1 teaspoon cornstarch, the salt, 1 teaspoon soy sauce and the pepper.
Cover and refrigerate 30 minutes.
Separate bok choy leaves from stems.
Cut leaves into 2-inch pieces; cut stems diagonally into 1/4-inch slices.
(Do not combine leaves and stems.) Cut onion into halves.
Place each half cut side down; cut into thin slices.
Mix 2 tablespoons cornstarch and the cold water.
Heat 2 tablespoons oil in 10-inch skillet or wok over high heat until hot.
Add beef mixture, gingerroot and garlic; cook and stir until beef is brown, about 3 minutes.
Remove beef from skillet with slotted spoon.
Add bok choy stems and onion; cook and stir 3 minutes.
Add bok choy leaves, pea pods and mushrooms; cook and stir 2 minutes.
Stir in chicken broth and 1 tablespoon soy sauce; heat to boiling.
Stir in cornstarch mixture; cook and stir 1 minute.
Stir in beef; heat just until beef is hot.