In a large pot, heat 2 tablespoons of olive oil over medium heat. Add the diced onions, sliced carrots, and sliced celery. Cook for about 5 minutes, or until the vegetables start to soften.
Add the minced garlic and cook for another 1-2 minutes, or until it becomes fragrant.
Pour in the chicken bone broth and add the chicken breasts or thighs, bay leaf, dried thyme, salt, and pepper. Bring the soup to a boil.
Once the soup is boiling, reduce the heat to a simmer. Cover the pot and let it cook for about 20-25 minutes or until the chicken is fully cooked and the vegetables are tender.
While the soup is simmering, prepare the gluten-free noodles separately according to the package instructions. Cook them in a separate pot of boiling water and strain them when they are done. Toss the cooked noodles with 1 tablespoon of olive oil to prevent sticking.
Once the chicken in the soup is fully cooked, remove it from the pot and shred it using two forks. Return the shredded chicken to the pot.
Remove the bay leaf from the soup.
To serve, place a portion of the cooked gluten-free noodles into each soup bowl.
Ladle the hot chicken soup over the noodles.
Garnish with fresh chopped parsley and serve with lemon wedges and gluten-free crackers or bread, if desired.