How to Make It
In a large enameled cast-iron casserole, heat the olive oil. Season the chicken with salt and pepper and cook over moderate heat, turning, until golden, about 8 minutes. Transfer to a large plate. Add the leeks and sliced celery to the casserole and cook, stirring occasionally, until softened, about 5 minutes. Add the mushrooms and garlic and cook, stirring occasionally, until the garlic is fragrant, 2 minutes. Add the thyme sprigs, stock, chicken and 2 quarts of water and bring to a simmer. Partially cover and simmer for 30 minutes; stir in the barley and cook until tender and the chicken is cooked through, about 1 hour longer. Transfer the chicken to a baking sheet; when cool enough to handle, discard the skin and shred the meat.
Discard the thyme sprigs. Add the egg noodles to the casserole and cook until al dente, then stir in the shredded chicken and the lemon juice and season with salt and pepper. Serve the soup garnished with chopped parsley, tarragon and celery leaves.