Mix all wonton ingredients except wrappers. Add ~1 tsp filling to each wrapper, wet the edges, fold and seal. Make ~20 for the soup; freeze the extras.
Bring a separate pot of water to a boil for the wontons and noodles.
In a large pot, sauté ginger, garlic, and scallions in olive oil for 2–3 min.
Add broth, mushrooms, water chestnuts, soy sauce, sesame oil, salt, and pepper. Bring to a boil, then simmer 2–3 min.
Add bok choy and cook 2–3 min. Add shrimp and the cornstarch slurry; boil 2–3 min until shrimp are pink, then turn off heat.
Boil wontons separately for 3–4 min, until the filling reaches 165°F (74°C), then add to the soup.
Cook noodles according to package directions. Drain and add to the soup, or keep separate and add to each bowl for firmer noodles.
