Place the chicken in a large pot and add the onion, carrots, garlic, and celery. Season with 1–2 teaspoons salt. Don’t go overboard with salting; it will cook down, and you can always add more later. Add a few cracks of black pepper. Bring to a boil and then cover, reduce heat, and simmer for 1 hour and 30 minutes.
Carefully remove the chicken from the pot using tongs. Transfer it to a large bowl and let it cool.
Return the broth to a rapid simmer over medium heat. Simmer for 30 minutes to reduce the broth further. It will be a dark golden brown.
Strain the broth into a large bowl through a fine-mesh sieve. Discard solids.
Pick the chicken from the bones and shred the meat with your fingers. Transfer the shredded meat to the bowl of strained broth to keep it moist. Reserve the carcass for stock if you like.