In a 5- to 6-quart pan over high heat, bring potatoes, broth, wine, and garlic to a boil. Cover, reduce heat, and simmer 15 minutes.
Meanwhile, rinse fish and cut into 4 equal pieces. Add to pan and return broth mixture to a boil over high heat; cover, reduce heat, and simmer just until fish is opaque but still moist-looking in center of thickest part (cut to test) and potatoes are tender when pierced, 10 to 12 minutes. With a slotted spatula, lift fish and potatoes from broth and arrange equally on plates; keep warm.
In a small bowl, mix cornstarch with 1 tablespoon water until smooth. Add to broth mixture over high heat and stir until mixture boils, about 1 minute. Stir in cilantro and add salt and pepper to taste. Spoon sauce equally over fish.