Step 1Quarter the chicken, removing the wings and the back (you can reserve these for making stock) and keeping the bones intact. Cut the thighs from the legs and cut the breasts in half through the ribs; you will have eight pieces. Pat the chicken dry, then season with salt and pepper.
Step 2Heat the oil in a 6-quart heavy-bottom lidded casserole and brown the chicken pieces over medium-high heat, turning them over so that they brown evenly, about 15 minutes.
Step 3Remove and reserve the chicken. Pour off all but about 1 tablespoon of excess oil from the pan. Add the leeks, fennel, garlic, rosemary and spring onions and saute over medium heat for about 2 minutes.
Step 4Return the chicken to the pan, along with any accumulated juices, and add 2 1/2 cups of water. Bring to a boil, then reduce to a simmer and cover and cook until the chicken is done, about 20 minutes. Stir in the carrots during the last 15 minutes of cooking.
Step 5Meanwhile, bring a pot of salted water to a boil. Blanch the favas for 1 minute then cool in an ice bath. Drain and then peel. Set aside.
Step 6When the chicken is cooked, remove the pieces and keep warm. Discard the rosemary. Add the peas and simmer uncovered for about a minute over medium-low heat.
Step 7To finish, add the favas, half of the parsley and yogurt to the pan of vegetables and broth, stirring to combine. Check for seasoning. To serve, spoon two pieces of chicken into the middle of each soup plate, then ladle the vegetables and broth around the chicken. Top with the remaining fresh parsley.