Bring a large pot of water to a boil. Add the noodles and cook as the label directs. Put the bok choy in a colander and pour the noodles on top to drain and wilt the bok choy. Rinse under cold water, drain well and set aside.
Meanwhile, heat the sesame oil in a medium saucepan over medium heat. Add the mushrooms, ginger and a pinch of salt. Cook, stirring, until the mushrooms soften and release their liquid, 3 to 5 minutes. Add 2 cups water, the chicken broth, soy sauce and chili-garlic sauce. Bring to a simmer and cook until slightly reduced, about 15 minutes; season with salt.
Divide the noodles and bok choy among shallow bowls. Ladle the soup over the noodles. Top with the roast beef slices, scallion and sesame seeds. Serve with more chili-garlic sauce.