In a large skillet over medium heat, combine parsley, green onions, salt, pepper, white wine and water; bring to a boil. Add flounder and poach for 8 to 10 minutes. Remove flounder to a lightly buttered shallow baking dish. Continue cooking wine mixture until liquid reduced to about 1 cup.
In a large saucepan melt 2 tablespoons of butter then add flour, stirring until a smooth paste is formed. Gradually add reduced liquid and heavy cream, stirring constantly over low heat. Continue cooking, stirring constantly, until thickened. Add remaining butter; pour over the flounder. Place the flounder under the broiler and broil until browned.
This baked flounder recipe serves 6.