Put chicken broth, ginger, and garlic in a wide pot with a lid. Bring the broth to a boil, reduce heat to medium-low, and simmer 3 to 5 minutes.
Stir soy sauce into the broth mixture; add catfish fillets. Spoon broth over the fillets. Place cover on the pot, bring broth to a boil, and let cook for 3 minutes more. Add mushrooms, cover, and cook until the fish loses pinkness and begins to flake, about 3 minutes more. Sprinkle green onion over the fillets, cover, and cook for 30 seconds. Garnish with cilantro to serve.