Prepare the green beans by cutting off the ends and chopping into bite-size pieces (maybe 1/2 inch or smaller). Blanch in boiling water for 2 minutes. Strain and immediately rinse in cold water (to stop the cooking process). Set aside.
Clean and slice up the mushrooms, discarding the center stem. Mince the garlic. In a large pot, melt the butter. Add the mushroom and garlic and cook for just a minute or two until the mushrooms begin to soften. Whisk in the flour and cayenne, this will become a paste. Season generously with salt and pepper. Then slowly whisk in the milk and vegetable stock so it incorporates well (you don't want a bunch of chunks of flour paste floating in the mixture). Then stir in 12 ounces of the shredded cheese. Once it begins to look melted, or mostly melted (sort of stringy on your mixing spoon), then stir in the green beans and noodles.
If you want to make this ahead, you absolutely can. Just don't top with the French fried onions until you are ready to bake. What kind of shredded cheese should you use? Really any kind you like. I prefer a mixture of pepper jack and sharp cheddar.