Cut the halibut fillets into 4-ounce pieces no thicker than 1-inch each.
In a large skillet over medium-low heat, heat the olive oil. Add the carrot, onion, celery, mustard seed and coriander seed. Sweat until vegetables are crisp-tender, about 7 minutes. Add the wine, vinegar and stock; bring to a boil. Season with salt and pepper, stir in half the basil and half the chervil.
Arrange the fish so it fits snugly in 1 layer in a casserole or baking dish. Pour the boiling marinade over the fish. The fish must be completely covered by the liquid, which will cook the fish as it cools. Allow to cool to room temperature, about 10 to 15 minutes. You can either serve immediately or serve chilled.
Remove the fish from the liquid and reserve the liquid to use as a dressing. Plate the fish and garnish with the carrots, celery and onions. In a salad bowl, toss the lettuces and remaining basil and chervil with some of the dressing. Serve alongside the fish and vegetables.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.