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1
Fill bowl with water and squeeze the lemon half into it. Working with 1 artichoke, 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. Scrape out the furry choke. Rub the artichoke heart all over with the lemon half and drop in the bowl of water.
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2
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, cut into 1/4-inch dice.
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3
Bring 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. Refrigerate until very cold, about 1 hour.
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4
Meanwhile, roast the pepper halves over a gas flame or under the broiler, skin side up, until nicely charred. Peel the peppers and cut them into 1/4-inch dice.
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5
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.
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6
In a large skillet, heat 1/4 inch of vegetable oil until shimmering. Lightly dust the dumplings with flour and fry. Cook over moderately high heat until they are golden brown, about 4 1/2 minutes.
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7
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.
