Place the chicken in a large pot and cover with 10 cups of water. Add more if needed to immerse the chicken. Add 3 teaspoons kosher salt, a head of garlic, the quartered shallot, and 2 bay leaves. Bring to a boil and skim off any foam from the surface of the broth. Reduce the heat to low, cover the pot, and simmer for 1 hour.
Carefully remove the chicken from the broth using tongs. Transfer it to a bowl. Return the heat on the pot of broth to medium and simmer rapidly for 20 to 30 minutes, until the liquid reduces to approximately 8 cups of broth. It’s okay if you have a little more or a little less. Turn off the heat.
Carefully strain the broth through a fine-mesh sieve into a large bowl. Set aside. Wipe out the pot used for the broth and return it to the stove. Discard the spent aromatics.
Once the chicken is cool enough to handle, pick the meat from the bones and shred the meat with your fingers or dice it with a knife. You should have 4 to 5 cups of meat. Set it aside.
Sauté the soup aromatics:
Add 1 tablespoon of extra virgin olive oil to the soup pot. Turn the heat to medium. Once hot, add the sliced leeks, diced celery, and minced celery leaves. Season with a pinch of salt. Sauté for 6 to 7 minutes.
Add the diced celery, minced celery leaves, and carrots. Season with a pinch of salt. Sauté for 3 to 4 minutes.
Add the garlic to the pot and sauté for 1 minute until fragrant. Add the carrots and sauté for 1 minute. Add a pinch of salt and pepper.
Simmer the soup:
Add the shredded chicken and 8 cups of homemade chicken broth. If you have a little more, you can add it to the pot or reserve it for another use. If you have a little less, supplement with water.
Bring the soup to a boil. Reduce the heat to low and simmer, uncovered, for 20 to 30 minutes or until the carrots are fork-tender.
Add the pearl couscous:
Add the pearl couscous to the soup and continue simmering for 12 to 15 minutes until tender. Taste and add salt and pepper.
Steep the saffron:
As the pearl couscous simmers, steep the saffron. Add the lightly crushed saffron to a small bowl. Cover with 2 tablespoons warm water. Let it stand for 5 to 10 minutes.
Finish the soup:
Taste the soup and add salt and pepper if needed. Turn off the heat. Add the bowl of steeped saffron and lemon juice. Let the soup stand for 5 minutes.
To serve:
Spoon the soup into bowls and enjoy!
Notes
Note 1: If you opt to skip this step, simply use a whole rotisserie chicken–you'll need 4 cups of meat total–and 8 cups of store-bought chicken stock.