In a large pot, add chicken, carrots, peas, chicken broth and water. Heat over medium high, bringing to a low boil. Cook for 10 minutes, then reduce to medium low and cook 15 minutes, stirring occasionally.
Taste the soup, and add seasonings as needed. If you are using your home made broth, it is likely well seasoned already. If not, add a little at a time until you like the taste.
Turn the heat to medium high and bring to a gentle boil. Slowly add tortellini, and stir. Boil for 8 minutes (or according to cooking time on package). Reduce heat, then simmer for 5 minutes.
Remove from heat, and serve with fresh chopped parsley and parmesan cheese.