Rinse fillets and pat dry. Place fish in a buttered baking pan. Season with pepper and spread 2 tablespoons of the softened butter or margarine over the fish.
Set aside, and preheat the oven to 425° F.
In a skillet, melt 3 tablespoons of butter and add the scallions. Cook for one minute. Add the remaining butter to the pan and add the mushrooms. Continue cooking and shaking the pan until the butter is absorbed. Add the dill and stir.
Spoon sauce over the fish fillets and bake for about 8 to 10 minutes or until fish turns opaque and flakes with a fork.
Baste fish several times during cooking with the accumulated pan juices.