Pat the chicken dry with paper towels and season generously all over with salt and peper; set aside

Heat the oil in a large skillet saucepan over medium-high heat until shimmering. Add the chicken and cook, turning occasionally, until it's browned all over, about 6-8 minutes. Transfer to a a large plate and set aside.

Reduce the heat to medium. Add carrots, celery, onion, salt, pepper, and thyme to the saucepan and stir to combine. Cook, stirring occasionally and scraping up any browned bits from the bottom of the pan, until the vegetables have softened and are just starting to brown, about 5 minutes.

Add the broth and stir to combine. Add the bay leaf and return the chicken pieces to the saucepan. Increase the heat to medium high and bring to a boil. Reduce the heat to medium-low and simmer until the chicken is cooked through, about 20 minutes. Turn off the heat.

Transfer the chicken to a cutting board. Using to forks, remove the meat from the bone, discarding the skin, cartilage, and fat. Shred the meat into bite-sized pieces and add it back to the saucepan.

Break the noodle block into large pieces, add them to the saucepan, and stir to combine. Let sit, stirring occasionally, until the noodles are cooked through, about 5 minutes. Add the parsley and stir to combine. Taste and season with salt and pepper as needed.