Heat oil in pressure-cooker pot over medium heat until shimmering. Add onions and cook until softened, for about 5 minutes. Stir in garlic and thyme and cook until fragrant, about 30 seconds. Stir in the carrots, celery, and soy sauce, scraping up any browned bits. Season chicken generously with salt and pepper and place breast side up in pot. Pour in the water. Your chicken should mostly be covered with the water. Be careful not to overfill your pressure cooker (there should be a line inside that indicates how high you can go!).

Lock pressure cooker lid in place and bring to high pressure over medium-high heat. Cook on high pressure for 20 minutes.

Use the quick-release pressure and then carefully remove lid, allowing steam to escape away from you.

Transfer chicken to carving board and let cool slightly. Using 2 forks, shred chicken into bite-size pieces, discarding skin and bones. Meanwhile, using large spoon, skim excess fat from surface of soup if necessary. Bring soup to boil, stir in noodles, and cook until tender, for about 5 minutes. Stir in shredded chicken and parsley, season with salt and pepper to taste, and serve.