Begin by fabricating your whole chicken into parts. You should have thighs, breasts, wings, and drumsticks. Rinse the chicken parts under cold water and pat them dry with paper towels.
In a large pot or Dutch oven, heat the olive oil over medium heat. Add the chopped onion and sauté for about 5 minutes, or until translucent. Stir in the minced garlic and cook for an additional minute until fragrant.
Place the chicken parts into the pot, skin-side down. Season with coarse salt and fresh cracked pepper. Let them sear for about 5-7 minutes without moving them, allowing the skin to brown nicely.
Add the chopped celery, carrots, and bay leaf to the pot. Pour in the chicken stock until the chicken is submerged. Bring the mixture to a gentle boil.
Reduce the heat to low and cover the pot. Let the chicken simmer for about 45 minutes to 1 hour, or until the internal temperature reaches 165°F (75°C).
Once the chicken is cooked, remove it from the pot using a slotted spoon and let it cool slightly. When cool enough to handle, shred the chicken using two forks or your hands.
You can use the shredded chicken immediately in your favorite recipes or store it in an airtight container in the fridge for up to 4 days. Alternatively, you can freeze it for longer storage.