Place the chicken in a large, heavy-bottomed pot. Cover with 12 to 16 cups of water until mostly submerged. It’s okay if a bit of the breast is exposed. Add the celery, onion, garlic, bay leaves, and salt. Bring to a boil. Reduce the heat to low and partially cover the pot. Simmer for 1 hour 30 minutes. Skim the top to remove foam or scum periodically.
Remove the lid. Use tongs to carefully lift the chicken from the pot and transfer it to a large bowl.
Turn the heat on the pot to medium and rapidly simmer for 20 to 30 minutes to reduce the liquid.
Once the chicken is cool enough to handle, remove the skin and pick the meat from the bones. Reserve the bones and skin for stock, if desired. Shred or chop the chicken into bite-sized pieces and set aside.
Strain the stock:
Scoop out the head of garlic and transfer it to a small bowl. Turn off the heat and strain the broth through a fine-mesh sieve into a large bowl. Discard the spent aromatics. You should have about 12 cups of stock. It’s okay if you have a little more or less. Wipe out the pot and return it to the stove.
Once the garlic is cool enough to handle, pop the cloves from the paper and mash them into a paste. Set aside.
Make the stew:
In the pot, heat 1 tablespoon extra virgin olive oil over medium heat. Add the diced onion, celery, carrots, and parsnips. Sauté for 8 to 10 minutes. Season with salt and pepper.
Add the herbes de Provence to the vegetables and sauté for 1 minute until fragrant. Add the potatoes and mashed garlic and season with a pinch of salt.
Simmer the stew:
Pour the reserved stock over the vegetables and bring to a boil. Add the shredded chicken. Reduce the heat to low and simmer, uncovered, for 30 minutes or until the potatoes are fork-tender. Skim off any excess fat from the top of the broth as it simmers.
Cook the pearl couscous:
Taste the soup and add more salt and pepper if needed. Turn the heat to medium. Once the liquid begins to bubble, add the pearl couscous and heavy cream. Simmer over medium heat for 12 to 15 minutes or until the pearl couscous is very tender. It will absorb much of the liquid, and the stew will be thick! Taste and season one more time.
Finish the stew:
Add the minced parsley and lemon juice to the pot. Turn off the heat.
To serve:
Ladle the stew into bowls and finish with more minced parsley. Enjoy!