In a large skillet melt the butter over medium heat and add the onion and raw chicken (if using leftover cooked chicken, don’t add it to the skillet now, you’ll add it later). Saute the onion and chicken, if using, until the onions are soft and translucent and the chicken is cooked through, about 5 to 6 minutes. Add the garlic and cook for about one minute, stirring, until fragrant.
Sprinkle the flour over the onions and chicken and stir to combine.
Cook over medium heat for one minute – this helps get rid of the starchy, flour taste.
Slowly whisk in the milk and chicken broth. Cook, stirring constantly with a whisk, and bring the sauce to a simmer over medium to medium-high heat. Add the salt and pepper. If you are using leftover cooked chicken, add it now. Continue simmering, stirring the sauce frequently, until the sauce has thickened, about 5-8 minutes.
Serve the chicken sauce over rice with your toppings of choice, such as olives, tomatoes, shredded sharp cheddar cheese, green onions, mandarin oranges and chow mein noodles.