Cook wild rice separately, in 4 cups water, about 45 minutes (follow package instructions)
Meanwhile, set a soup pot over medium heat and add butter and oil
Add onion, carrot, celery and mushrooms and season with salt and pepper, saute 15 minutes or until starting to brown, stirring frequently
Reduce heat to medium low, add garlic, Italian seasoning, and flour. Cook 1 minute more while stirring to incorporate flour
Add the chicken, stock and milk. Whisk to combine, scraping any bits off the bottom
Bring to a boil, then lower the heat and simmer on low until the soup thickens, about 30 to 45 minutes
Wild rice can be added when it's done, anytime while the soup is simmering. If the soup is too thick, adjust by adding more stock or milk. Serve with crackers or crusty bread