How to Make It
Fill a small bowl with water and squeeze the lemon half into it. Working with 1 artichoke at a time, snap off the outer leaves. Using a sharp knife, trim the stem and base of the artichoke and cut off the top two-thirds of the leaves. With a spoon or melon baller, scrape out the furry choke. Rub the artichoke heart all over with the lemon half and drop in the bowl of water. Repeat with the remaining artichoke.
Bring a small saucepan of water to a boil. Add the artichoke hearts and simmer over moderately high heat until tender, about 12 minutes. Drain and cut into 1/4-inch dice.
Bring a medium saucepan of salted water to a simmer. In a large bowl, mix the ricotta with the Parmesan and 1 tablespoon of the flour; season with salt and pepper. Stir in the egg yolk and the diced artichoke hearts. Using 2 large serving spoons, form the mixture into 12 oval-shaped dumplings. Add the dumplings to the simmering water and cook gently until they start to rise to the surface, about 1 minute. Using a slotted spoon, transfer the dumplings to a large, rimmed baking sheet. Pat dry with paper towels and refrigerate until very cold, about 1 hour.
Meanwhile, roast the pepper halves over a gas flame or under the broiler, skin side up, until nicely charred. Transfer the peppers to a bowl, cover with plastic wrap and let cool. Peel the peppers and cut them into 1/4-inch dice.
In a small saucepan, combine 1/4 cup of the olive oil with the lemon juice, water, 1 tablespoon of the vinegar and the preserved lemon rind and boil over moderately high heat until reduced by half, about 3 minutes. Remove from the heat and whisk in the butter, 1 piece at a time. Stir in the shallots, olives, parsley, chives, tarragon and roasted peppers and season with salt and pepper. Keep the sauce warm.
In a large skillet, heat 1/4 inch of vegetable oil until shimmering. Lightly dust the dumplings with flour and add them to the hot oil. Cook the dumplings over moderately high heat until they are golden brown all over, about 4 1/2 minutes. Transfer to paper towels to drain.
In a medium bowl, combine the remaining 2 teaspoons of olive oil and 1 teaspoon of vinegar and season with salt and pepper. Add the arugula and toss. Spoon the lemon sauce into 4 shallow bowls. Arrange 3 dumplings in each bowl, mound the arugula alongside and serve.
Preserved lemon are lemons that have been cured in a lemon-salt mixture. They have a strong, pungent flavor. Look for them at specialty-food shops.