Turn the Instant Pot on and set it to sauté. Once it says hot, add the olive oil and heat until warm. Add the carrots, celery, onion, and garlic. Season them with basil, parsley, thyme, salt, and pepper. Sauté until the vegetables are soft, about 5 minutes.
Add the chicken broth and bay leaves to the pot, stirring to combine everything well. Place the chicken breasts on top of the mixture.
Put the top on and seal it properly. Set it to manual high pressure for 5 minutes. Make sure the valve is set to sealed before starting.
Once the cooking time is complete and you've heard that glorious beep again after 5 minutes, carefully perform a manual pressure release by turning it to venting.
Remove the chicken from the Instant Pot and set aside. Let it cool slightly before shredding it into bite-sized pieces.
Turn the Instant Pot back to sauté mode again. Once the liquid inside is boiling, add in your chosen noodles. Boil according to package instructions until they're al dente.
After cooking the noodles, remember to remove those bay leaves! Add back in your shredded chicken and stir everything together gently.