Place the chicken bones into a large, heavy-bottomed stockpot and cover with cold water, about 4 liters. Bring to a gentle simmer over medium heat, and skim off any foam that rises in the first 15 minutes.
Add the halved onion, crushed garlic cloves, thyme sprigs, and splash of apple cider vinegar to the pot. Lower the heat to maintain a gentle simmer, uncovered, for at least 4 hours, allowing the flavors to meld and the broth to deepen.
After simmering, turn off the heat and carefully strain the broth through a fine mesh strainer into another large pot or bowl, discarding solids. Set aside.
While the broth is still warm, add sliced carrots and celery to the strained stock. Return to low heat and simmer gently for another 30 minutes, until the vegetables are tender and the broth is flavorful.
Taste the broth and season with salt and pepper as needed, adding slowly to control the flavor. Let the soup sit for a few minutes to allow flavors to meld.
Serve the healing chicken soup hot, with a clear, golden broth filled with soft vegetables and herbal notes, offering a comforting, nourishing experience.