Preheat the oven to 200°C.
Parboil the potato in a large saucepan of salted, boiling water for 10 minutes. Drain and allow to cool to one side.
Butterfly the sea bass with a sharp knife (you can ask your fishmonger to do this for you). Drizzle half of the olive oil inside the fish and stuff with half the parsley. Season the insides well. Make a few diagonal slashes in the skin of the fish.
Rub the rest of the olive oil and parsley into the slashes. Season well and sit in a roasting tray. Pour over half the lime juice. Roast for 30 minutes uncovered.
Remove the fish from the oven and cover well with tin foil. Melt the butter in a large frying pan set over a moderate heat. Add the diced potato once the butter stops foaming. Sauté for 4-5 minutes until golden brown in colour all over, tossing and stirring frequently.
Drizzle the roast sea bass with the rest of the lime juice. Carefully lift onto serving platters and serve the sautéd potatoes on top and around. Tie the lime halves in rinsed pieces of muslin and serve on the side.