Season both sides of the chicken pieces generously with coarse salt and freshly cracked black pepper.
Heat the olive oil in a large sauté pan, rondeau, or saucepot over high heat until it shimmers and begins to smoke lightly.
Place the chicken in the hot pan skin-side down, reduce heat to medium-high, and cook undisturbed for 3–4 minutes until the skin is golden brown.
Flip the chicken pieces, add the chopped onion, garlic, bay leaf, celery, and carrots, and cook 3–4 minutes to sear the bottom of the chicken and soften the vegetables.
Pour in the chicken stock and gently season again with salt and pepper if needed.
Cover with a lid and simmer over low–medium heat for 40–45 minutes, or until the chicken is fork-tender and cooked through.
Remove the chicken from the braising liquid and let it cool at room temperature for about 10 minutes.
Strain the braising liquid through a fine-mesh strainer and reserve the stock for other uses or storage.
Remove and discard the skin and bones, then shred the chicken using your hands or two forks.
Use the shredded chicken immediately in recipes or store as desired.
