Scrub potatoes. Remove any bad spots. Do not peel. Cut each in half.
In a covered saucepan, boil potatoes in just enough water to cover the pieces. When they are fork-tender (about 15 to 20 minutes), remove from heat and drain. Set aside. (Note: you can also pierce whole potatoes with a knife or fork in several places and cook in microwave without water until fork tender, then cut each in half).
Meanwhile, in a skillet sprayed with non-stick cooking spray, combine cooked meat, broccoli, onion, carrots and water.
Boil until vegetables are fork tender - about 5 minutes. Reduce heat to low.
Combine milk, flour and pepper. Mix well.
Stir flour mixture into meat mixture until well blended.
Stir in cheese. Cook over low heat about 5 minutes longer or until sauce thickens, stirring frequently.
To serve, place 2 potato halves on each plate and mash the middle somewhat. Spoon about one third cup of the meat mixture over each potato half.
Cover and refrigerate leftovers within 2 hours.