Heat olive oil in a large Dutch oven over medium heat. Add diced onion and cook for 6 to 7 minutes until soft and slightly translucent. Add carrots and celery and cook 3 minutes more. Add garlic and stir for 60 seconds until fragrant.
Nestle bone-in chicken thighs skin-side up into the pot. Pour chicken broth over everything until the chicken is just covered. Add dried thyme, dried parsley, bay leaves, salt, and pepper. Bring to a full boil over medium-high heat.
Reduce heat to medium-low. Maintain a gentle simmer with the lid slightly ajar. Cook for 25 to 30 minutes until chicken thighs reach an internal temperature of 74°C (165°F) at the thickest point. For optimal shredding texture, cook to 82 to 85°C (180 to 185°F).
Lift chicken from the pot with tongs and transfer to a cutting board. Remove and discard bay leaves. Rest chicken for 5 minutes, then remove and discard the skin and bones. Shred meat with two forks into even pieces.
Skim visible fat from the surface of the broth with a wide spoon. Bring broth back to a gentle simmer over medium heat.
Add egg noodles to the simmering broth and stir immediately. Cook uncovered for 8 to 10 minutes, stirring every 2 minutes, until noodles are just tender with a slight chew.
Return shredded chicken to the pot. Stir to combine and cook on low for 2 minutes until warmed through. Taste and adjust salt and pepper.
Stir in fresh parsley. Turn off heat and rest 5 minutes before ladling into bowls.