Gather the ingredients.
Grease a shallow baking dish with the solid butter . Position a rack in the center of the oven and heat to 325 F/165 C.
Cut 1 ½ pounds flounder fillets into 4 same-size portions.
Arrange the pieces in the prepared baking dish, and sprinkle with 1 teaspoon fine salt, or to taste, and ⅛ teaspoon freshly ground black pepper.
In a small bowl or measuring cup, combine the remaining ¼ cup melted unsalted butter, 2 tablespoons freshly squeezed lemon juice, and 2 teaspoons minced onion.
Pour the lemon-butter mixture over fish.
Sprinkle with 1 teaspoon paprika.
Bake until the fish is cooked through and flakes easily with a fork, 15 to 25 minutes, depending on the thickness of the fillets. Meanwhile, make the garlic aioli, if desired.
Garnish with 1 tablespoon finely chopped parsley and lemon slices or wedges. Serve with garlic aioli, if using.
Gather the ingredients.
Crush 2 medium cloves garlic, transfer to a medium bowl, and mash well with a fork. Alternatively, use a mortar and pestle.
Add ½ cup mayonnaise, 2 tablespoons olive oil, and 1 tablespoon freshly squeezed lemon juice to the bowl. Stir well to blend.
Season with fine salt, to taste.
Cover and chill until serving time.
