Preheat the oven to 200°C.
Combine the diced root vegetables, onion, and garlic in a deep roasting tin.
Drizzle with olive oil and season with salt and pepper.
Stir the vegetables over medium heat on the stove until they begin to sizzle.
Roast in the oven for 35 to 40 minutes, stirring occasionally until tender.
Boil shallots, vinegar, lemon zest, lemon juice, and wine until reduced to 30ml.
Add 15ml cold water and boil again until only 15ml of liquid remains.
Whisk in cold butter cubes one at a time over low heat until the sauce is thick.
Season to taste and strain the sauce through a sieve into a clean pan.
Reduce the oven temperature to 180°C.
Fry cod fillets skin-side down in oil and butter until crisp, then brown the other side.
Roast cod in the oven for 4 to 5 minutes until the flesh is opaque.
Divide ratatouille among plates, top with cod, and spoon over the lemon beurre blanc.