Methods/steps

Preheat oven to 400°. Clean fennel thoroughly in cold water, cut off root end and cut bulb in half, lengthwise. Remove the core from both halves, then peel away sections and slice lengthwise into ¼-inch julienne.

Heat a heavy-bottomed skillet over medium heat and add 1 tablespoon olive oil. When oil is hot, add fennel with a pinch of salt and fresh ground pepper, toss well to coat with oil and continue to sauté 2–3 minutes, without allowing to color. Carefully add about ¼ cup of water to skillet, turn heat to low and cover with a tight fitting lid. Steam for 3 minutes, then remove from heat and reserve.

Wash celery root thoroughly in cold water, then, with a heavy, sharp knife, cut off the bottom and top of the root to make a flat, stable surface. Place celery root on a cutting surface and cut away the rough exterior skin in strips—following as closely as possible the shape of the celery root. Use a paring knife to trim whatever bits of skin remain, then carefully cut the celery root into ?-inch-thick slices. Stack 2 or 3 slices together and cut into ?-inch julienne, then set aside.

Preheat a deep fryer to 325° (a cast-iron skillet over medium-high heat with 1 inch of peanut oil can substitute). Divide fennel evenly into 4 ceramic or other heavy, nonreactive ovenproof dishes that are only slightly larger than the fish fillets. Distribute the Pernod and the crème fraiche among the dishes (and a splash of white wine, if you like).

Rinse grouper in cold water and dry thoroughly with paper towels. Season fish all over with coarse sea salt and fresh ground pepper to taste. Divide fish among the prepared dishes and sprinkle the tops with remaining olive oil. Place all 4 dishes on a sturdy, rimmed baking pan for easier transport. Place the pan in the oven and roast for 20–25 minutes, depending on the thickness of the fish, until done. (The fish will begin to flake when gently squeezed and will have just become opaque all the way through, but should be quite moist.)

While fish is baking, fry celery root until golden—about 1 minute. Remove with a slotted spoon and shake off excess oil. Toss in a bowl with a pinch of salt.

When fish is done, remove pan from oven and allow to rest briefly. Serve in dishes used for cooking if you like (carefully place dish on a plate) or use a spatula to remove fish to warmed plates. Spoon fennel and any juices remaining in the dish around fish and top with fried celery root and chopped parsley.