Preheat the broiler and set a rack 2 inches from the heat.
Toss the beans with the oil, 3/4 teaspoon salt and 1/2 teaspoon pepper. Place them on a rimmed baking sheet in a single layer. Broil the beans until crisp tender and charred in places, about 4 minutes.
Stir together the cilantro stems and mayonnaise. Sprinkle each fillet with a generous pinch each of salt and pepper, and then divide the cilantro mixture among the fillets, spreading to cover. Place the fillets over the beans and continue to broil until the fish is just cooked through, 4 to 5 minutes.