Place the whole chicken or chicken parts into a large stockpot and cover with cold water. Turn the heat to medium and bring to a gentle simmer, creating a soft bubbling sound.
Skim off any foam that rises to the surface during the first 10 minutes; this keeps your broth clear and clean.
Add quartered onion, smashed garlic cloves, and sliced ginger to the pot. Let everything simmer gently for about 1.5 hours, with the lid slightly ajar to prevent boiling over.
Remove the chicken from the broth and set aside to cool slightly. Once cool enough to handle, shred the meat into bite-sized pieces, discarding the bones.
Strain the broth through a fine-mesh strainer into a clean pot, discarding the solids. Return the clear broth to the stove and bring it back to a gentle simmer.
Add the shredded chicken, sliced carrots, and celery to the simmering broth. Cook for about 20 minutes until the vegetables are tender and the flavors meld.
Season the soup generously with salt and pepper, tasting as you go to reach your preferred level of seasoning.
Stir in freshly chopped herbs and lemon zest for brightness and freshness, and cook for another 2 minutes to release their flavors.
Serve the soup hot, with a sprinkle of extra herbs or lemon zest if desired, enjoying the comforting aroma and nourishing warmth.