Preheat oven to 350°F (175°C) and grease a 2-quart baking dish.
In a large skillet, brown the ground beef over medium heat. Remove and set aside.
In the same skillet, add butter and sauté sliced potatoes, celery, carrots, green bell peppers, and onions for 5 minutes.
Add water, cover, and simmer the vegetables for 10 minutes until softened.
In a large bowl, mix the browned beef, sautéed vegetables, and undiluted cream of mushroom soup.
Spread half of the chow mein noodles in the prepared baking dish.
Pour the beef and vegetable mixture on top and spread evenly.
Cover with foil and bake for 20 minutes.
Remove the foil, sprinkle with shredded cheddar cheese and the remaining chow mein noodles.
Bake uncovered for an additional 10-12 minutes until the cheese is melted and bubbly.
Serve hot and enjoy!