In a large pot, saute onion, celery, carrots and mushrooms in butter for about 4-5 minutes adding carrots, celery and mushrooms first then adding onions a minute later. Cook until translucent.
Next whisk in flour. Cook for a minute, stirring frequently.*
Add shredded chicken, chicken stock and Marsala then bring to a boil. Reduce and simmer for 5 minutes.
Stir in cooked rice and milk and bring to a boil. Reduce heat and let simmer 5 more minutes then it's ready to serve. Add salt and pepper to taste.
Video
Notes
You can purchase rotisserie chicken already shredded to save time.
You want to cook the flour in the butter until it bubbles for about one minute. This cooks out the floury taste.