Strip the meat from the rotisserie chicken, discard the skin, and cut it into bite-sized pieces. Set aside.
Place the chicken bones in a pot with the broth and water. Simmer on low for 30–40 minutes to extract extra flavor. Strain and discard the bones. This step can be done in advance to save time.
Heat olive oil in a large Dutch oven or soup pot over medium-high heat.
Add the onion, carrots, celery, and garlic. Cook, stirring occasionally, until the vegetables soften, about 8 minutes.
Pour in the broth, making sure the total liquid equals 8 cups. Bring to a simmer, cover, and let cook for 15–20 minutes.
Stir in the chopped chicken, poultry seasoning, salt, and pepper. Increase heat to bring it to a boil.
Lower the heat and let it gently simmer for another 10 minutes.
Cook the egg noodles according to package directions. Drain and rinse under cool water.
Add the peas and cooked noodles.
Adjust seasoning as needed, garnish with fresh parsley, and serve hot.