1. In 10-inch skillet over medium heat, in 3 tablespoons hot butter or margarine, cook mushrooms and green onion until tender, stirring occasionally.
2. Preheat broiler if manufacturer directs. Place fillets in broiling pan; dot fillets with 1 tablespoon butter or margarine. Broil 10 minutes or until fish flakes easily when tested with a fork.
3. Meanwhile, in 2-quart saucepan over low-heat, melt 1/4 cup butter or margarine (1/2 stick); stir in flour, salt, and pepper until smooth. Gradually stir in cream and wine; cook, stirring constantly, until cream mixture is very thick and smooth.
4. When fish is done, with pancake turner, carefully transfer fillets to broiler-safe platter and top with cream mixture. With slotted spoon, spoon mushroom mixture over cream mixture; sprinkle with cheese. Broil 3 minutes or until cheese is melted and browned.