In a large stockpot, add chicken broth, carrots, and chicken breasts. Add salt and pepper to taste. Bring to a boil, then cover and simmer for 30 minutes, or until carrots are tender.
While carrots and chicken simmer, stir together baking mix and milk until dough forms.
Remove chicken from broth and set aside. Add frozen peas to pot and return to boil. Tear off grape-sized balls of dough and drop into boiling broth (or roll and cut dough into uniform dumplings if you prefer). Stir as needed to ensure dumplings are submerged.
Shred chicken with two forks and stir into broth with dumplings. Reduce heat and simmer 10 minutes more.
You can substitute canned biscuit dough for the baking mix dumplings if you prefer.