Step 1Heat the oven to 375 degrees. Place 2 tablespoons of the olive oil and 1 tablespoon of the butter with the garlic in a small saucepan. Heat over low heat until the butter is melted. Cook for about a minute more until the garlic is fragrant, then remove from the heat.
Step 2Wash the chicken under cold water and pat dry with paper towels. Brush the chicken with the garlic mixture. Season each chicken leg with one-fourth teaspoon salt and allow to stand at room temperature while you prepare the lemons and artichokes for frying.
Step 3Fill a large bowl with cold water and halve one of the lemons, squeezing the juice from one half into the water. Trim the artichokes down to the hearts: Using a sharp knife, cut away the tough outer leaves until you see only light green at the base. Cut away about the top half-inch of the artichoke tip. Trim the end of the stem, then peel the stem and base of the artichoke; there should be no dark green tough spots left, only pale green and ivory. Place the peeled artichokes into the bowl of lemon water.
Step 4When all of the artichokes are trimmed, slice them lengthwise no thicker than one-fourth inch, using a mandoline or by hand with a sharp knife. As you slice them, return them to the bowl of lemon water.
Step 5Using a mandoline or a sharp knife, slice two of the lemons crosswise into slices no thicker than one-fourth of an inch. Set aside.
Step 6Drain the artichokes well and pat them dry. Place the cream and flour into separate medium bowls and one by one dip the artichoke and lemon slices into the cream. Let any excess cream drain off, then dip the slices into the flour to coat, shaking off any excess flour. Set them on a wire rack until you are ready to fry them.
Step 7Heat a large heavy skillet with the remaining 2 tablespoons olive oil and 1 tablespoon butter over medium-high heat until hot. Add the chicken pieces in batches and cook until browned on both sides, about 3 minutes per side. Adjust the heat as necessary. Put the browned chicken in a large shallow baking pan. Wipe out the skillet with a paper towel and set aside for the pan sauce.
Step 8Roast the chicken until tender and a thermometer inserted into the meatiest part of the thigh (not touching the bone) reaches 165 to 170 degrees, about 30 to 35 minutes.
Step 9While the chicken is roasting, fill a large, heavy stock pot with enough oil for deep-frying (the oil should come about 3 inches up the sides of the pan). Heat the oil until a thermometer inserted reads 350 degrees. Add the lemon slices in batches to the deep fryer and cook until the slices are golden brown and puffed on both sides, about 1 1/2 minutes total. Fry the artichokes until lightly browned on both sides, about 1 minute total. Drain on paper towels and sprinkle lightly with salt. Set aside in a warm place until ready to serve.
Step 10Remove the cooked chicken from the oven and drizzle the pieces with the juice from the remaining half of the lemon. Remove the chicken from the pan and set aside in a warm place. Pour the chicken broth over the baking pan to loosen the juices and browned bits. Stir in the wine, then pour all of the liquid back into the saute pan. Bring the sauce to a boil, then reduce the heat and simmer for 1 to 2 minutes, until slightly reduced. Swirl the remaining teaspoon of butter into the sauce, bit by bit, to thicken. Remove from the heat and strain the sauce through a fine mesh strainer. Set aside in a warm place.
Step 11To serve, place one chicken leg on each of four plates and spoon some sauce over it. Divide the lemons and artichokes evenly among the servings. Sprinkle each chicken piece with a few chervil leaves and serve immediately.