Bring a large pot of salted water to a boil. Peel and quarter potatoes, and introduce into boiling water; cook until tender, about 15 minutes. Drain and mash. Set aside.
In a large skillet over medium-high heat, cook ground beef and onion until beef is brown. Drain. Stir in tomato soup and green beans. Pour into a 9x13 baking dish. Mound mashed potatoes in a ring around the meat mixture (do not cover meat). Sprinkle potatoes with shredded cheese.
Bake in preheated oven 30 minutes, until potatoes are golden.