5 large carrots (about 1 pound), 1 halved lengthwise and 4 cut into 1/2 -inch
5 celery ribs (about 1 pound), 1 halved lengthwise and 4 cut into 1/2 -inch
5 large flat-leaf parsley sprigs, plus 2 tablespoons finely chopped parsley
2 bay leaves
1 teaspoon whole peppercorns
1 tablespoon unsalted butter
1 large Spanish onion, quartered through the root end
2 pounds large Yukon Gold potatoes, peeled and cut into 1/2 -inch dice
Freshly ground pepper
Lemon wedges, for serving
Cut the breasts off the chickens and discard the skin. Cut the meat into 1-inch pieces and refrigerate.
Put the chicken halves in a large soup pot. Add the water, carrot and celery halves, parsley sprigs, bay leaves and peppercorns.
Melt the butter in a medium skillet. Add the onion quarters and cook over moderately high heat until browned, about 5 minutes; add to the soup pot. Season with salt and bring to a boil. Skim the broth and simmer over moderately low heat until the chicken falls off the bone and the broth is flavorful, about 3 1/2 hours. Let cool slightly.
Strain the broth into a large saucepan and skim off the fat. Bring the broth to a boil. Add the diced celery and cook for 3 minutes. Add the diced carrots and cook for 5 minutes. Add the potatoes and cook for 5 minutes. Season the reserved breast meat with salt and pepper, add it to the soup and simmer until it is cooked through and the vegetables are tender, about 5 minutes. Season the soup with salt and pepper, sprinkle with parsley and serve in bowls. Pass the lemon wedges at the table.