1. Heat oil in a large Dutch oven coated with cooking spray over medium-high heat; sauté mushrooms and ginger 5 minutes or until liquid evaporates and mushrooms darken.
2. Add broth, 3 cups water, and soy sauce; bring mixture to a boil. Stir in bok choy and next 3 ingredients; cover, reduce heat, and simmer 3 minutes or until shrimp are done. Stir in lime juice just before serving.