In a large pot, combine chicken pieces and water. Bring to a boil over high heat, then reduce heat to low, skim off any foam, and simmer for 30 minutes.
Remove chicken from the pot and set aside to cool. Strain the broth through a fine-mesh sieve into a clean pot; discard solids.
Heat olive oil in the same pot over medium heat. Add onion, carrots, and celery; sauté for 5-7 minutes until softened.
Add garlic, thyme, and bay leaf; cook for 1 minute until fragrant.
Pour in the strained broth and bring to a simmer.
Shred the cooled chicken, discarding skin and bones, and return the meat to the pot.
Add egg noodles and cook for 8-10 minutes until tender.
Season with salt and pepper to taste. Remove bay leaf.
Serve hot, garnished with fresh parsley.
Notes
Store leftovers in an airtight container in the refrigerator for up to 4 days. Reheat gently on the stove or in the microwave.