Pat chicken thighs dry, season generously with salt and pepper. Heat olive oil in a large Dutch oven over medium-high heat. Place thighs skin-side down and cook until deep golden brown, about 5-6 minutes. Flip and cook 3 minutes more. Transfer to a plate.

Reduce heat to medium. Add onion, carrots, and celery to the same pot. Cook, stirring occasionally, until softened, about 5 minutes. Add garlic and cook 30 seconds until fragrant.

Return chicken thighs to the pot. Pour in chicken broth, add thyme and bay leaves. Bring to a boil, then reduce heat to low, cover, and simmer gently until chicken is cooked through and tender, reaching an internal temperature of 165°F (74°C), about 20 minutes.

Remove chicken from the pot to a cutting board. Let cool slightly, then discard skin and bones. Shred meat into bite-sized pieces using two forks.

Bring the broth back to a boil. Add egg noodles and cook according to package directions (about 6-8 minutes) until just al dente. Stir in shredded chicken and simmer 2 minutes to heat through.

Remove bay leaves. Taste and adjust seasoning with salt and pepper. Ladle into bowls, sprinkle with fresh parsley, and serve immediately.