Preheat oven to 375 degrees F. Spray a 9 x 13″ baking dish with cooking spray.
In a large skillet, melt butter over medium heat. Stir in mushrooms and garlic, and saute for about two minutes. Stir in flour until smooth. Stir in milk about ¼ c. at a time, stirring constantly to avoid lumps. Add half and half, salt, and pepper to taste. Bring to a simmer.
Stir in cheese until melted. Stir in frozen green beans, and transfer mixture to prepared baking dish. Arrange onion rings over the top, and bake in preheated oven for 30-40 minutes. Press onion rings down into the casserole a bit about halfway through baking. Casserole is done when it is bubbly and onion rings are golden brown.
You can use all milk instead of milk and half and half if you prefer, but the sauce won’t be quite as rich.