1 large egg yolk
1 tablespoon fresh lemon juice
1 tablespoon cornstarch
Set aside 1 teaspoon of the chopped rosemary. In a wide, shallow bowl combine the remaining rosemary, the garlic, 1/2 teaspoon of salt and 1 tablespoon of the olive oil.
Add the lamb and coat it well on all sides with the herb mixture. Cover and chill for at least 1 hour, and up to overnight.
Set an oven rack 4 inches from the broiler heating element. Heat the oven to broil.
In a small bowl, toss the artichokes with the remaining 2 teaspoons of oil and salt and pepper to taste. Arrange the artichokes in a single layer on a rimmed baking sheet.
Broil, turning them several times, until they are golden around the edges, about 3 to 4 minutes. Remove the pan from the broiler and set aside.
In a small saucepan over medium, heat the chicken broth until it is simmering. In a small bowl whisk together the egg yolk, lemon juice, reserved teaspoon of rosemary and the cornstarch.
Add a little of the chicken stock to the mixture in a stream, whisking. Add the egg mixture back to the chicken stock and cook for 1 minute, or until the sauce starts to bubble.
Season with salt and pepper, then stir in the artichokes. Keep warm over low heat.
Heat a grill or a grill pan over medium-high heat. Wipe off most of the garlic herb mixture from the lamb and spray the meat with olive oil cooking spray. Add the lamb to the grill pan.
Reduce the heat to medium and cook, turning once, about 4 minutes per side for medium-rare. Transfer the lamb to a plate, cover loosely with foil and let rest for 5 minutes.
Slice the lamb against the grain into slices about 1/4-inch thick. Add the lamb juices from the plate to the artichoke lemon sauce. Divide the sliced lamb between 4 serving plates and spoon sauce over each plate.