Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil; lightly coat with about 1 teaspoon butter.
Lay fish in a single layer on the prepared baking sheet.
Mix Parmesan cheese, 1/3 cup butter, mayonnaise, green onion, lemon juice, dill, salt, black pepper, and hot sauce together in a bowl.
Broil fish in the preheated oven until it flakes easily with a fork, 7 to 8 minutes. Gently spread Parmesan cheese mixture over fish; return to oven and broil until topping is bubbling and lightly browned, about 2 more minutes.