Heat the oven to 425°F and line a large rimmed sheet pan with parchment paper.
Toss the potatoes with 1 1/2 tablespoons olive oil, 1/2 teaspoon salt and 1/4 teaspoon black pepper, then arrange them cut-side down.
Roast the potatoes for 20 minutes, until their bottoms begin to brown.
Turn the potatoes, add the cod and asparagus, and coat both with the remaining olive oil, salt and black pepper.
Press the Parmesan over the tops of the cod fillets and scatter any remainder over the asparagus.
Roast for 12 to 15 minutes more, until the cod flakes and reaches 145°F and the asparagus is tender.
