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