Heat the large heavy-bottomed pot over medium heat and add a splash of olive oil. Once shimmering, place the chicken thighs in the pot, skin-side down if skin-on, and cook for about 5 minutes until golden brown. Flip and brown the other side for another 3-4 minutes. Remove the chicken and set aside.
Add the diced onion and minced garlic to the same pot, stirring with the wooden spoon. Cook for 2-3 minutes until fragrant and the onion becomes translucent, with some bits sticking to the bottom for flavor.
Pour in the chicken broth, scraping the bottom of the pot to loosen any browned bits. Bring the broth to a gentle simmer.
Return the browned chicken thighs to the pot, along with chopped thyme. Cover and let simmer gently for 20-25 minutes until the chicken is cooked through and tender.
Remove the chicken thighs from the broth and set aside to rest for a few minutes. Meanwhile, season the broth with salt and pepper to taste, and add the lemon zest or juice for a bright, fresh flavor.
Shred the chicken thighs into bite-sized pieces with two forks, discarding any excess fat or bones. Return the shredded chicken to the broth, stirring to combine.
Sprinkle chopped parsley over the soup for a fresh, herbal finish. Give everything a gentle stir and taste again, adjusting seasoning if needed.
Serve the hot soup in bowls, garnished with extra parsley if desired. Enjoy the comforting, aromatic flavors that fill your kitchen!