Preheat the oven to 375 degrees F (190 degrees C).
Cook ground beef in a skillet over medium-high heat until evenly browned. Drain excess grease. Season with garlic, salt and pepper. Stir in the onion soup, Worcestershire sauce and mustard, and bring to a boil. Mix together the cold water and flour, and stir into the sauce. Simmer over low heat for a few minutes, then set aside.
Meanwhile, place potatoes in a saucepan and add enough water to cover. Bring to a boil, and cook for 3 minutes, not until tender. Drain.
Spread half of the beef mixture in the bottom of a 9x13 inch baking dish. Arrange half of the potatoes over the beef. Cover with a layer of mixed vegetables. Repeat layers.
Cover the dish, and bake for 50 minutes in the preheated oven. Uncover, and sprinkle shredded cheese over the top. Bake for an additional 10 minutes to melt cheese.
