Heat oil in pressure cooker pot over medium heat until shimmering (For the Instant Pot, I use the saute button). Add the onion (and a pinch of salt) and cook until softened, about 5 minutes. Stir in garlic and thyme and cook until fragrant, about 30 seconds. Be careful not to brown the garlic. NOTE: I sometimes add dried thyme, and that is fine. I
Stir in water, carrots, celery, and soy sauce, scraping up any browned bits.
Season chicken with salt and pepper and place, breast-side up, in the pot (or just add cut-up chicken parts). Putting the chicken breast side up ensures more even cooking of the chicken. NOTE: As an alternative, buy a cut up chicken, as this makes shredding the cooked meat a lot easier to do.
After adding the chicken, be sure that the contents of the pot do not exceed the max fill level of your pressure cooker.)
Lock pressure cooker lid in place and bring to high pressure over medium-high heat for a stove top PC. As soon as the pot reaches high pressure, reduce heat to medium-low and cook for 20 minutes, adjusting heat as needed to maintain high pressure. NOTE: For the Instant Pot, set on SOUP function and it works perfectly.
Remove pot from heat. Quick release pressure, then carefully remove the lid, allowing steam to escape away from you. (Follow your pressure cooker’s manual for quick-release instructions.) NOTE: The first time I filled my pot with 8 cups of water, which was just below the max line. When I did a manual pressure release, a lot of liquid spurted out-- and I had to put a towel around the lid, so as not to risk being burned by hot liquid. Be careful!
Transfer chicken to cutting board, let cool slightly, then shred meat into bite-size pieces, discarding skin and bones. (I went for big chunks of chicken.)
OPTIONAL: Using a large spoon, skim excess fat from the surface of the soup. Bring soup to boil, stir in noodles, and cook until tender, about 5 minutes.
While the chicken is cooling, turn on the saute' function of your pressure cooker until the broth is bubbling. Add the egg noodles and cook for 4-5 minutes.
Stir in shredded chicken and parsley. Taste to determine if you need to season with salt and pepper to taste, and serve.