Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x13 inch baking dish; set aside
Bring a large saucepan of salted water to a boil. Add potatoes and cook until tender but still firm, about 15 minutes. Drain and mash.
Place lean ground beef and onion in a large skillet. Cook and stir over medium high heat until beef is evenly browned and onion is tender. Drain fat and stir in carrots, green beans, cream of mushroom soup and tomato soup.
Pour mixture into the prepared baking dish and top with mashed potatoes. Sprinkle with Cheddar cheese and bake in preheated oven for 30 minutes, or until potatoes are lightly browned.