Fill a large bowl with water, and squeeze lemon halves into water. Drop in lemon halves. Working with 1 artichoke at a time, remove tough outer leaves. Trim pointy tops and stems, and slice in half lengthwise. Transfer artichokes to the lemon water to prevent discoloration.
Heat a large high-sided skillet over medium-high. Add the butter, 3/4 of the fennel slices, and the shallot. Cook, stirring frequently, until shallot is golden in places, about 5 min.
Pour the wine into the skillet, and boil until evaporated, about 1 min. Drain the artichokes, and add to the skillet along with the stock, carrots, turnips, and preserved-lemon flesh. Return to a boil. Reduce heat to medium-low, and cover. Simmer until vegetables are tender, about 15 min. Season with salt (if necessary) and pepper.
Meanwhile, on a work surface, finely chop the remaining fennel slices, and scrape into a small bowl. Add the preserved-lemon peel, fennel fronds, basil, pine nuts, olive oil, and 1 Tbsp. lemon juice to the bowl with the fennel. Toss to combine. Season with pepper, and let marinate while vegetables cook.
Spoon cooked artichoke mixture into shallow bowls, and top with fennel relish. Serve with baguette.
Recipe by Laura Rege.