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 want to cook the flour in the butter until it bubbles for about one minute. This cooks out the floury taste.