Preheat oven to 450. On a large rimmed baking sheet, toss mushrooms with 2 tablespoons olive oil and rosemary; season with salt and pepper. Roast until tender and browned, tossing occasionally, about 15 minutes.
Push mushrooms to sides of pan; place cod in center and season with salt and pepper. Roast until opaque throughout, 8 to 10 minutes.
Meanwhile, in a small bowl, whisk together remaining oil, lemon juice, mustard, and parsley; season with salt and pepper. Serve with cod.