Heat olive oil in a large pot over medium heat. Add onion, carrots, and celery. Cook 6 to 8 minutes until softened. Add garlic and stir for 1 minute.
Add chicken pieces, water or broth, bay leaves, thyme, parsley stems, 1½ tsp salt, and black pepper. Bring to a full boil.
Skim grey foam from the surface. Reduce heat to low, partially cover, and simmer 35 to 40 minutes until chicken reaches 75°C (165°F) at the thickest point.
Remove chicken with tongs. Cool 5 minutes, then shred the meat. Discard skin, bones, bay leaves, and parsley stems.
Return broth to a rolling boil. Add egg noodles and cook 6 to 8 minutes until tender with a slight bite.
Return shredded chicken to the pot. Taste and adjust salt. Serve hot, topped with fresh parsley leaves.
