Heat the olive oil and butter in a Dutch oven set over medium heat. Add the chopped onions, sliced celery, and carrots; cook for 5 minutes, stirring occasionally. Stir in the garlic and cook for another 20 seconds until fragrant.
Add the chicken broth and stir all the browned bits from the bottom of the pot. Incorporate thyme sprigs and bay leaves; then increase the heat to high and bring everything to a simmer.
Add in the chicken breasts along with salt and pepper; stir everything well before covering. Simmer over medium heat for about 25 to 30 minutes until the chicken is fully cooked through.
Carefully remove the chicken breasts from the pot and transfer them to a cutting board. Allowing them to cool slightly makes shredding easier later on.
If using regular egg noodles, add them now to the broth and cook for about 6 to 7 minutes until they’re al dente. If using Carba-Nada noodles, wait until you shred your chicken before adding them.
While waiting on those noodles, shred your chicken using two forks or your hands after discarding any bones. Stir this shredded goodness back into your soup; cover again and let it simmer for another couple of minutes.
Remove your Chicken Noodle Soup from heat and discard both thyme sprigs and bay leaves. Taste it now; adjust salt and pepper as needed. Ladle into bowls, garnish with fresh parsley, and serve alongside lemon wedges.