In a large oven safe skillet, brown ground beef, onions, and mushrooms until beef is cooked through and vegetables are tender.
Drain excess fat. Add garlic and cook for another minute.
Stir in flour and cook for another minute.
Whisk in broth, milk, salt, and pepper.
Add green beans and cook mixture until thickened.
Remove from heat and stir in 1 cup cheese and sour cream.
Shred potatoes with a grater or food processor and squeeze out excess liquid.
Top casserole with shredded potatoes and remaining ½ cup cheese.
Bake at 350 degrees for 30 minutes or until potatoes are tender. I like to broil the casserole for another couple of minutes at the end to crisp the top.