Set your Instant Pot to "Sauté" mode and melt the butter. Add the onion, carrots, and celery, cooking for 4-5 minutes until slightly softened.
Add the garlic and cook for another minute until fragrant.
Pour in the chicken broth and add the chicken breasts, bay leaves, thyme, parsley, salt, and pepper. Stir to combine.
Close the lid, set the valve to "Sealing," and cook on high pressure for 8 minutes.
When done, carefully quick-release the pressure. Remove the chicken breasts and shred them with two forks.
Set the pot back to "Sauté" mode and add the egg noodles. Cook for 6-8 minutes, stirring occasionally, until noodles are tender.
In a small bowl, whisk together the heavy cream and flour until smooth. Stir this mixture into the soup and cook for 2-3 minutes until thickened.
Return the shredded chicken to the pot, remove bay leaves, and stir well. Taste and adjust seasoning if needed. Garnish with fresh parsley before serving.