Boil the potatoes in salted water for 10-15 minutes, then drain.
Boil the broccoli for 8-10 minutes, adding asparagus, beans, and peas at 2-minute intervals.
Fry the turbot in butter skin-side down for 2 minutes, flip, and cook for 1 minute.
Soften shallots in butter in a medium-hot pan for several minutes.
Reduce the white wine by half, then the fish stock by half, and the cream by one-third.
Sauté the cooked potatoes in oil for 2-3 minutes before adding the boiled vegetables and butter.
Reheat the sauce to a simmer and stir in the champagne and chives.
Plate the vegetables, top with fish, pour over the sauce, and garnish with chervil.