Heat the oven to 220°C/gas 7. Remove excess bones from the fish, then dry the fish with kitchen paper. Score the skin with a sharp knife to stop the fillets curling while cooking.
Place the carrots, wine and herbs in a large baking dish, cover with a lid or sheet of baking paper or foil folded into place, and place in the oven to cook for 15 minutes.
Heat the olive oil in a large frying pan, then cook the fillets skin-side down for 1 minute. Turn and cook for another minute. Cook the fish in batches, keeping the pan really hot to seal in the juices. As soon as all the fish is seared, take the carrots out of the oven and add the fish, skin-side up. Add more wine if necessary. Add the peas and asparagus to the dish, drizzle with olive oil and baste the vegetables and fish with the wine and oil. Return to the oven without any cover and roast for 7 minutes. Season, and serve the fish with the vegetables and any remaining juices.