In a large pot, combine chicken, broth, and 8 cups water. Bring to a boil; reduce to a rapid simmer and cook until chicken is cooked through (skim off foam), about 18 minutes. With tongs, transfer chicken to a rimmed baking sheet and refrigerate 10 minutes.
Add carrots to pot and cook until crisp-tender, about 10 minutes. Add pasta and cook until tender, about 8 minutes. Remove skin and bones from chicken and discard; refrigerate 4 thighs for Chicken and Sweet Potato Hand Pies. Shred remaining chicken and add, along with peas, to pot. Cook until heated through. Season to taste with salt and pepper.