Place the bone-in chicken pieces in a heavy-bottomed pot and brown them over medium heat until golden brown on all sides, about 8 minutes, listening for a satisfying sizzle and watching the skin develop a deep color.
Remove the chicken and set aside. In the same pot, add chopped carrots, celery, and a pinch of salt, sautéing until they release their aroma and begin to caramelize slightly, about 10 minutes, with a gentle sizzle and fragrant smell filling the air.
Add minced garlic to the vegetables and cook for another minute until fragrant; the mixture should smell bright and look slightly glossy.
Pour in the chicken broth, scraping the bottom of the pot to loosen any browned bits, creating a rich base. Bring the broth to a gentle simmer, watching for small bubbles to rise slowly.
Return the browned chicken to the pot, cover with a lid, and let everything simmer gently for about 30 minutes, until the chicken is cooked through and the flavors meld, filling the kitchen with a comforting aroma.
Remove the chicken from the soup, shred the meat off the bones using tongs or forks, and return the shredded chicken to the pot, stirring gently to combine.
Add chopped greens to the soup and cook for an additional 5 minutes until wilted but still vibrant and fresh-looking.
Season the soup with salt and pepper gradually, tasting as you go, until the flavor feels balanced and bright.
Just before serving, squeeze fresh lemon juice into the soup, stirring gently to brighten all the flavors and add a zesty finish.
Ladle the steaming soup into bowls, ensuring each serving has a good mix of chicken, vegetables, and greens, and enjoy the comforting, layered flavors that come alive with each spoonful.
