Heat oven to 400° F. Rub the cod with the oil and season with ¼ teaspoon salt.
Dip the tops of the fish (not the side from which the skin has been removed) in the cornflakes and place on a parchment- or foil-lined baking sheet.
Bake the fish until just cooked through and opaque, about 10 minutes.
Meanwhile, steam the broccoli until tender, 4 to 6 minutes.
In a small saucepan over medium heat, melt the butter. Stir in the Parmesan and ¼ teaspoon salt.
Divide the fish and broccoli among plates. Serve with the sauce in small ramekins for dipping.