Prepare the following vegetables, adding them all to the same bowl: Dice 1 large yellow onion (about 2 cups) and 3 medium celery stalks (about 1 cup); peel and cut 2 medium carrots into ½-inch thick rounds (about 1 ½ cups). Mince 2 garlic cloves and set aside separately.
Heat 2 tablespoons olive oil in a 6-quart or larger electric pressure cooker or Instant Pot with the Sauté function. Tlt the insert to coat with the oil. Add the onion, celery, carrot, 1 ½ teaspoons kosher salt, and ¼ teaspoon black pepper. Cook, stirring occasionally, until the vegetables are tender, 6 to 8 minutes. Stir in the garlic, 1 teaspoon dried thyme, and 2 bay leaves, and cook for 1 minute more. Turn the pressure cooker off. Add 1 ½ pounds boneless, skinless chicken thighs, 1 box chicken broth, and 2 cups water.
Lock on the lid and make sure the pressure valve is set to seal. Set to cook for 10 minutes under HIGH pressure. It will take about 20 minutes to come up to pressure. Meanwhile, coarsely chop ¼ cup parsley leaves and squeeze 2 tablespoons lemon juice.
When the cook time is up, let the pressure naturally release for 10 minutes. Quick release any remaining pressure. Transfer the chicken with tongs to a clean cutting board. Remove and discard the bay leaves.
Turn the pressure cooker back on to Sauté and bring the soup to a boil. Add 6 ounces egg noodles (about 4 heaping cups) and cook uncovered until just tender, about 5 minutes. Meanwhile, shred the chicken with two forks.
Return the shredded chicken to the pot and stir in the parsley and lemon juice. Serve immediately.
