Chicken a la King

My wife's long time classic. Inexpensive, comforting and delicious!
Boil then simmer a whole chicken for about an hour, let cool, separate the pieces of meat from the bones, skin etc., saving the broth.
Make a white sauce:
Melt 5 Tablespoons butter (or margerine) in a medium size sauce pan.
Whisk in 5 Tablespoons flour.
Gradually add 2 cups milk while whisking.
It's ready when it has thickened.
In a large stainless steel or enameled pot cook 1-2 minced garlic cloves in a little oil until softened and lightly golden. add 1 1/2 cups of the chicken broth, a package of frozen mixed vegetables (corn, carrots, peas, cut string or lima beans optional) and simmer to warm and cook. Add the white sauce, a can of cream of mushroom soup. Stir until smooth and hot.
Add the chicken pieces, more broth if desired, salt and pepper (we use white) and serve over steamed rice.