Fill a large bowl with 1 quart of water, and squeeze 2 lemon halves into it. Add the squeezed lemon halves to the water.
Working with 1 artichoke at a time, bend back the outer leaves close to the base until they snap off where they break naturally. Discard the layers until the exposed leaves are pale green at the top and pale yellow at the base. Using a small sharp knife, trim the stem and the base until it is smooth and no dark green areas remain. Trim the leaves. Rub the base with the remaining lemon halves. Cut the artichoke lengthwise into 4 wedges. Using a small knife, cut out the choke and the small purple-tipped leaves; then halve again for a total of 8 wedges. Place the artichoke wedges in the lemon water.
Heat the olive oil in a large skillet over medium heat. Add the shallots and cook, stirring often, until softened, about 3 minutes. While the shallots are cooking, drain and rinse the artichokes. Add the artichokes and the potatoes to the skillet and cook, stirring, for 1 minute. Pour in the wine and simmer until the liquid is reduced to a few spoonfuls, about 6 minutes. Add the stock and bring to a boil. Add half of the asparagus, fava beans, and peas, cover the skillet, and simmer the stew for 10 minutes. Stir in the remaining asparagùs, fava beans, and peas, 2 tablespoons of the chives, and 2 tablespoons of the parsley. Let the mixture simmer, partially covered, for about 4 minutes, or until the potatoes and artichokes are tender. Stir in the remaining herbs and the grated Grana Padano, and season with salt and pepper to taste. Serve topped with shaved Grana Padano.
High-quality frozen fava beans do not require any work. Add them to the soup after they have thawed out. If you buy fresh fava beans, cook the shelled beans in boiling salted water for 3 minutes, or until just tender. Drain, and cool in a bowl of ice water. Then drain, and peel off their tough outer skin (it should slip off easily).
• Add your favorite spring vegetable to this stew, such as sliced carrots or sugar snap peas.
• Add protein: this dish can quickly turn into a fricassee when some bite-size pieces of cooked chicken are added to the vegetables.
• Substitute thawed frozen artichokes for the fresh ones; it will cut down on the prep time considerably.
• Substitute basil and tarragon for the chives and parsley.