Stir together miso, ginger, cilantro, and 1 Tbsp. shallot in a bowl. Coat each fish fillet with mixture. Cover and refrigerate 6 hours. Bring fava beans, broth, 1/2 c shallots, and thyme to a boil in medium saucepan. Lower heat; simmer until beans are very tender, about 10 min. Drain excess broth, leaving enough to just cover the beans. Stir in butter; season with salt and pepper. Remove cod from marinade. Heat oil in nonstick skillet. Cook cod until browned and firm, turning once, about 4 min. per side.
To serve, using a slotted spoon, divide fava beans among 4 plates. Top with cod and serve.