Bring 1.5 quarts of water to a boil in a medium saucepan. Add noodles and simmer, uncovered over medium heat until just al dente (6-9 minutes). When the noodles are done, drain and set them aside.
Heat the oil in a wok or large skillet. When the oil is hot, add the bok choy and sauté over medium high for 30 seconds. Add vegetable broth, soy sauce, ginger, and garlic. Toss the bok choy to coat and simmer 1-2 minutes over high heat, until most of the broth has evaporated.
Add the cooked noodles to the pan and cook, tossing everything together, until the noodles are hot, 1-2 minutes.