Line a small plate with plastic wrap. Carefully remove the skin on the halibut (you could also ask our seafood department to do this for you). Set the halibut on the plate. Set the halibut in the freezer until almost frozen solid (that will make it easier to slice).
Transfer fish to a cutting board. With a very sharp knife, cut the halibut, widthwise, into 16 thin slices. Set the slices in a sided dish (a glass pie plate works well). Combine the juices, oil, mustard, fennel seed, tarragon and cayenne in a small bowl. Pour mixture over the fish, ensuring it is evenly dispersed. Cover, refrigerate and marinate fish 4 hours, or until it is “cooked” by the acidity of the citrus juice and turns opaque.
Fan 4 slices of the fish on each of 4 well-chilled plates. Divide and mound some lettuce on the other side of the plate. Arrange the tomato, cucumber and carrot on and around the salad greens. Drizzle the fish with some of its marinade, season with salt and pepper, and serve.