Preheat the oven to 180C/350F/Gas 4.
For the haddock, heat the oil in an ovenproof frying pan over a medium heat. Fry the haddock skin-side down first for 2-3 minutes, then turn it over and continue to cook for a further 2-3 minutes, or until the fish has browned. Season to taste with salt and freshly ground black pepper.
Transfer the fish to the oven to cook for 6-8 minutes, or until it has cooked through.
For the Vichy carrots, simmer the carrot batons, butter, water and cardamom pods in a covered saucepan over a medium heat, and simmer with the lid on for 6-7 minutes, or until the carrots are tender.
To serve, spoon the Vichy carrots onto a serving plate with the roasted haddock, and garnish with the lemon wedges.