Place a large stockpot on the stove and pour in about 2 liters of water, then bring it to a gentle simmer over medium heat.
Add the chicken pieces to the simmering water along with a pinch of salt, and let them cook gently for about 45 minutes, skimming off any foam that rises to the surface.
While the chicken simmers, prepare the vegetables by peeling and slicing the carrots and celery into small, even pieces to ensure they cook uniformly.
Once the chicken has cooked through and the broth is rich and aromatic, carefully remove the chicken pieces from the pot and set aside to cool slightly.
Strain the broth through a fine sieve into a clean container to remove any solids, then return the clear broth to the original pot.
Add the sliced carrots, celery, and minced garlic to the strained broth, then bring to a gentle simmer for about 15 minutes, until the vegetables are tender and fragrant.
Meanwhile, shred the cooked chicken into bite-sized pieces, discarding skin and bones if any are present.
Add the shredded chicken back into the soup, along with chopped parsley and thyme sprigs, then season with salt and pepper to taste. Let everything simmer together for another 5 minutes.
Squeeze fresh lemon juice into the soup to brighten the flavors, stirring gently to combine.
Taste and adjust the seasoning with salt and pepper as needed, then ladle the hot, clear soup into bowls, ready to serve.
