Place chicken in a large pot and cover with 12 cups water. Add onion, carrots, garlic, celery, bay leaves, and thyme. Add 1 teaspoon salt (you'll add more later). Ensure the chicken is covered with water. Bring to a boil and then reduce heat to low. Cover and simmer for 1 hour and 30 minutes.
Carefully remove the chicken from the pot and transfer it to a large bowl.
Turn the heat on the broth to medium. Allow it to rapid-simmer for 30 minutes so that it reduces further. The broth will be a very deep golden brown. You should be left with between 8–10 cups of broth.
Strain the broth through a fine-mesh sieve into a very large bowl. Discard solids.
Shred the chicken from the carcass and place the meat in the bowl of broth (I do this to keep it moist.). Set aside.
Carefully wash out the pot and return it to the stovetop.