Place first 4 ingredients in a Dutch oven; cover with 8 cups water. Bring to a boil; cover, reduce heat, and simmer 1 hour or until chicken is done. Transfer chicken to cutting board; remove chicken from bones, discarding bones. Coarsely chop chicken.
Strain broth through a sieve over a bowl, discarding vegetables and solids. Return broth to pan. Add chopped chicken, bouillon granules, salt, and pepper.
Bring to a simmer; add wonton wrapper halves, 1 at a time, to broth. Simmer 8 minutes; stir in parsley.