Bring a large pot of lightly salted water to a boil. Add potatoes, and cook until tender but still firm, about 15 minutes; drain, and return to pan.
While potatoes are boiling, heat oil in a large skillet. Cook ground beef with onion, red pepper, and garlic until beef is evenly brown. Stir in beef broth, ketchup, soy sauce, Worcestershire sauce, and curry powder. Bring to a boil, and simmer 3 to 4 minutes. Mix cornstarch with a little water to form a paste, then stir into skillet with tomatoes, peas and carrots. Cook until thickened; season with salt and pepper. Spoon into a casserole dish.
Preheat oven on broiler setting. Add milk and butter to cooked potatoes, and whip until smooth and creamy. Spoon over meat mixture. Sprinkle top with shredded cheese.
Place under broiler for 3 to 5 minutes, or until cheese is melted and speckled with brown.