1 large carrot (of as uniform thickness as possible)
1 2 1/2-inch-thick wedge of savoy cabbage
1 small leek
4 - 6 baby turnips
1 - 2 celery stalks
4 - 6 small fingerling or marble potatoes (no wider than 1/2 inch in diameter)
1 tablespoon extra virgin olive oil
1 tablespoon unsalted butter
2 ounces Bayonne ham or prosciutto (not sliced)
2 large garlic cloves, peeled and thinly sliced
Kosher salt and freshly ground black pepper
1-ounce piece of Parmigiano-Reggiano cheese or piece of Parmigiano rind
8 cups chicken stock or vegetable stock
1 pound fava beans in the pod
16 medium asparagus spears
24 small shiitake mushrooms, cleaned
2 tablespoons chopped Italian parsley
2 tablespoons minced chives
FOR THE SOUP: You will need 1/2 cup of each of the sliced vegetables for the soup.
Peel the carrot and cut away the ends. Cut it lengthwise in half, then cut each half lengthwise again to give you 4 pieces. Cut each piece crosswise into 1/4-inch-thick slices.
Remove any dark green outer leaves from the cabbage and reserve for another use. Place the wedge cut side down on a cutting board and cut crosswise into 1/4-inch-wide slices.
Cut away the dark green leaves and root end of the leek. Cut the leek lengthwise in half and rinse well under cold water. Cut each piece of leek lengthwise in half and then cut crosswise into 1/4-inch-wide slices.
Peel the baby turnips. Cut off the tops, then cut them into small wedges, about 1/2 inch thick.
Wash and trim the celery. Use a paring knife to pull away the strings, then cut the stalks into 1/4-inch-thick slices.
Wash the potatoes. Cut away and discard the ends, then cut the remaining potatoes into 11/2-inch-thick slices.
Heat the olive oil and butter in a large saucepan over medium heat. Add the ham skin or fat side down and the garlic and swirl the pan for a few seconds to coat the garlic, then sweat the garlic for a minute or two.
Add the 1/2 cup each carrot, cabbage, leek, turnips, and celery, stir, and season to taste with salt and pepper. Cook gently for 2 to 3 minutes. Add the 1/2 cup potatoes, the sachet, Parmigiano, and stock and bring to a simmer.
Add salt and pepper to taste and simmer for 20 to 30 minutes, until the potatoes are tender.
Meanwhile, prepare an ice bath. When the potatoes are tender, pour the soup into a bowl or other container and chill in the ice bath until cold, then cover and refrigerate until ready to serve. (The soup is best if it is refrigerated for a day.)
FOR THE GARNISHES: Prepare an ice bath.
Shell the fava beans and peel the skins from the beans (peeling the beans before cooking them prevents gases from being trapped between the beans and their skins that could cause discoloration).
Remove the small germ at the side of each bean. (You should have about 1 cup of beans.) Blanch the beans in a large pot of generously salted water for about 5 minutes or until tender. Using a skimmer, immediately transfer to the ice bath to chill.
Cut away the bottom third of each asparagus spear and discard. Cut the remaining spears on a sharp bias into pieces about 1/4 inch thick and 11/2 to 2 inches long. Blanch the asparagus in boiling water until tender. Transfer to ice bath to chill.
When they are cold, drain the favas and asparagus and spread on paper towels to drain. Cut off and discard the mushroom stems, then cut the mushrooms into 1/4-inch-thick slices.
TO COMPLETE: If any fat has solidified on the surface of the soup, remove and discard it. Transfer the soup to a saucepan, and remove and discard the sachet and Parmigiano.
Remove the ham, cut away any excess fat, and cut into lardons about 11/2 inches long and 1/4 inch thick. Return the lardons to the soup and bring the soup to a boil.
Add the mushrooms to the soup, reduce the heat, and simmer for a minute. Add the fava beans, asparagus, and tomato confit and remove from the heat. Stir in the parsley and chives, taste the soup, and adjust the seasoning.
Ladle the soup into bowls and garnish each bowl with a few shavings of Parmigiano-Reggiano and a drizzle of olive oil.