Heat the Instant Pot using the Sauté function.
Add the olive oil, carrots, celery, and onion. Cook, stirring occasionally, until the vegetables are tender and starting to brown, about 5 minutes.
Add the garlic and cook for an additional minute.
Next, add the chicken, chicken stock, water, Italian seasoning, and bay leaf.
Attach the lid and ensure the valve is in the sealing position.
Set the Instant Pot to Pressure Cook - Manual for 12 minutes.
Once the instant pot has finished cooking, allow the pressure to release naturally for 10 minutes.
Release any additional pressure manually by switching the valve to the venting position.
Remove the chicken and bay leaf. Set the Instant Pot to the Sauté function again and add the egg noodles. Cook according to the package directions-- or just until the noodles are soft.
While the noodles cook, shred the chicken. Once the chicken has been shredded, add it back to the Instant Pot and stir to combine. Season with salt and pepper to taste.
Enjoy warm. Store any leftovers in an airtight container in the fridge for up to three days.