Brown the chicken. Pat the chicken thighs dry with paper towels. Heat the olive oil in a large skillet over medium-high heat. Add the thighs skin-side down and cook for 5–7 minutes, until golden. Turn and cook for another 2 minutes. Transfer to a plate, reserving the fat in the skillet. The chicken will finish cooking in the broth.
Soften the vegetables. Transfer 2 tablespoons of the fat from the skillet to a large soup pot. Add the butter and onion. Cook over medium heat for about 4 minutes, stirring occasionally. Add the carrots and celery and cook for another 3 minutes.
Add the garlic and broth. Stir in the garlic, thyme, and black pepper and cook for 30 seconds, until fragrant. Pour in the chicken broth and add the bay leaves. If using unsalted broth, add 1 teaspoon of fine salt now and adjust the seasoning at the end.
Simmer the chicken. Add the browned thighs and any juices from the plate. Bring to a gentle simmer, partially cover, and reduce the heat to low. Simmer for 30–35 minutes, or until the chicken is tender and separates easily from the bone. Allow a little longer if needed.
Shred the chicken. Transfer the thighs to a plate. Once cool enough to handle, remove and discard the skin and bones. Shred the meat into bite-size pieces. Remove the bay leaves from the soup and skim off any excess surface fat.
Cook the noodles. Add the egg noodles to the simmering soup and cook according to the package directions, checking for tenderness a minute early. Return the shredded chicken during the last 1–2 minutes to warm through.
Finish and serve. Remove from the heat and stir in the parsley. Taste and adjust the salt and pepper, then serve promptly.