Heat the olive oil in a large Dutch oven or stockpot over medium heat. Add the onion, carrots, and celery and cook, stirring occasionally, for 6-7 minutes, until softened. Add the garlic and thyme and cook for 1 minute more.
Pour in the chicken broth and add the chicken breasts. Bring to a gentle simmer over medium-high heat, then reduce the heat to medium-low and simmer for 15 minutes, until the chicken reaches 165 °F in the thickest part.
Transfer the chicken to a cutting board and shred it with two forks. Keep the broth at a gentle simmer.
Stir in the egg noodles and cook for 6-7 minutes, until tender.
Return the shredded chicken to the pot, add the peas, and cook for 2 minutes. Season with salt and pepper to taste, stir in the parsley, and serve hot.