Pull all the meat off the rotisserie chicken, shred it into bite-size pieces (about 4 cups), and refrigerate. Reserve the carcass, bones, skin, and juices for the broth.
Peel and slice the carrots into 1/4-inch rounds, slice the celery to match, dice the onion, mince the garlic, and finely chop the fresh parsley.
Heat the olive oil in a Dutch oven over medium heat. Add the onion, carrots, and celery and cook 4 to 5 minutes, stirring often, until softened and translucent.
Stir in the garlic, dried parsley, thyme, oregano, salt, pepper, and bay leaf. Cook 1 minute, stirring constantly, until fragrant without browning the garlic.
Pour in the broth and scrape up any browned bits. Add the reserved carcass, bones, skin, and juices, pushing them down to submerge. Bring to a boil, then reduce to medium-low, cover, and simmer gently 25 to 30 minutes.
Turn off the heat. Use tongs to lift out the carcass, bones, and skin, then discard them along with the bay leaf. Taste the broth and add a pinch more salt if it tastes flat.
Return the pot to a boil, stir in the egg noodles, and simmer uncovered about 7 minutes. Stir in the shredded chicken and cook 3 to 5 more minutes, until the noodles are al dente and the chicken is hot, about 10 to 12 minutes total.
Remove from the heat and stir in the fresh parsley. Taste and adjust salt and pepper, then ladle into warm bowls and serve right away.