Melt half of the butter in a large stockpot over medium heat. Add next 4 ingredients and cook until onions are translucent. Add remaining butter. When butter is melted, sprinkle flour over vegetables and stir often for 3 minutes. Stir in 1/2 cup chicken stock and continue stirring until smooth. Add remaining chicken stock, a little at a time, while stirring. Add mushrooms and milk, bring to a boil and simmer for 10 minutes. Stir in rice and turkey to warm. Season with salt and pepper.