-
Preheat oven to 450degrees F. Coat a rimmed baking sheet with cooking spray.
-
Toss potatoes and broccoli with 1 tablespoon oil and 1/4 teaspoon salt in a large bowl. Transfer to the prepared baking sheet. Cook, stirring once, until tender, 20 to 25 minutes.
-
Meanwhile, pat cod dry and cut into 4 portions. Season with the remaining 1/4 teaspoon salt and pepper. Heat 1 tablespoon oil in a large nonstick skillet over medium heat. Add capers and cook until golden brown, 1 to 2 minutes. Using a slotted spoon, transfer the capers to a paper towel, leaving the oil in the pan. Place the cod skin-side down in the pan. Cook, undisturbed, for 5 minutes. Flip and cook until the fish flakes easily with a fork, 3 to 4 minutes more.
-
Combine the remaining 2 tablespoons oil, lemon juice, mustard and garlic in a small bowl.
-
Toss the potatoes and broccoli with thyme. Serve the vegetables and cod drizzled with the lemon vinaigrette and garnished with the capers and Parmesan.