Drop noodles into a large quantity of boiling water – at least 2 quarts – and cook 3 1/2 to 5 minutes, until barely tender to the bite. Drain, rinse with cold water and reserve.
Place the mushrooms in a bowl and add boiling water to cover. Let stand 15 to 30 minutes, until tender, then drain and squeeze the mushrooms to extract most of their moisture. Cut off and discard the tough stems and julienne the caps.
Combine the beef and oyster sauce in a bowl; stir to coat. Let stand for 10 minutes.
In another bowl, combine the chicken broth, soy sauce and sesame oil. Set aside.
Heat a wok over high heat. When hot, add the vegetable oil, swirling to coat the sides. Add the garlic, ginger, and green onions and cook, stirring until fragrant, about 30 seconds. Add the beef and cook, stirring constantly, about 1 minute. Add the mushrooms and bok choy and cook for a minute longer. Add the sauce and noodles. Gently toss until heated through and sauce has thickened. Serve immediately.