FOR THE CHICKEN STOCK: Heat 2 tablespoons olive oil in a large stockpot. Add half the onions, carrots, celery, and all of the garlic. Saute for 1-2 minutes.
Add the chicken pieces, bay leaves, thyme, salt, and pepper. Cover with 12 cups water, bring to a boil, reduce the heat, cover with a lid, and simmer for 1 1/2 hours. Taste for seasoning during the time it is simmering and adjust the salt and pepper, as needed.
Remove the chicken pieces and set aside to cool enough to handle. When cool, remove the skin and bones and shred the chicken with your hands. Reserve 2 cups for the soup.
Strain the stock and set aside until you are ready to prepare the soup.
FOR THE SOUP: Heat 1-2 tablespoons of olive oil in the stockpot. Add the remaining vegetables and saute for 5-6 minutes until the vegetables are beginning to get tender.
Add the chicken and 8 cups of stock to the pot. Additional thyme may be added if desired. Simmer for 10-15 minutes.
Add the noodles and cook for the recommended time on the package.
Serve with freshly chopped parsley, if desired.