Melt butter over medium heat in a dutch oven or large pot. Add chicken and cook for 4-5 minutes until almost cooked on all sides.
Add onion, carrots, and celery, and cook for 5 minutes, until softened and fragrant.
Add Italian seasoning, chicken broth, and milk and bring to a boil.Add orzo. Reduce heat and simmer, covered, for 15-20 minutes, or until orzo is soft and creamy.
Be sure to stir frequently to prevent the pasta from sticking to the bottom of the pan. Remove from heat and stir in cheese, lemon, and parsley if using.
Notes
You shouldn't need it but if all the liquid gets absorbed before the orzo is done cooking, add an additional ½ cup of broth or water.
Transfer any leftovers to an airtight container and store in the refrigerator for 3-5 days. To reheat, microwave briefly or in a skillet with a little bit of liquid (water or broth).
If intending to freeze some, set aside a portion without the cheese. Transfer to a freezer-safe container and freeze for up to 3 months.