Heat a heavy-bottomed pot over medium heat and add olive oil. Once shimmering, place the chicken thighs skin-side down and cook until golden brown, about 5 minutes per side. Remove and set aside.
Add chopped carrots, celery, and a pinch of salt to the same pot. Sauté until the vegetables are fragrant and slightly softened, about 8-10 minutes, stirring occasionally. The vegetables should be tender but still hold some texture.
Stir in minced garlic and cook for 30 seconds until fragrant, taking care not to burn it. You’ll notice the garlic becoming aromatic and slightly golden.
Pour in the chicken broth, then return the browned chicken thighs to the pot, skin side up. Bring the mixture to a gentle simmer, skimming off any foam that rises to the surface.
Reduce the heat to low, cover partially, and let the soup simmer gently for about 1.5 hours, until the chicken is tender and falling off the bone. Check occasionally and skim any foam.
Remove the chicken thighs from the soup, shred the meat with tongs or forks, discarding bones and skin. Return the shredded chicken to the pot and stir well.
Squeeze fresh lemon juice into the soup, then season with salt and pepper to taste. Stir to combine, and let the flavors meld for a couple of minutes.
Finish by sprinkling chopped parsley over the soup for a fresh, herby touch, and give it a gentle stir.
Ladle the hot soup into bowls, making sure each serving contains plenty of tender vegetables and shredded chicken. Serve immediately and enjoy the comforting aroma and rich flavors.