Put the diced potatoes in saucepan; add enough water to barely cover. Bring to boil. Reduce the heat and simmer, covered, until soft, about 15 minutes. Drain the potatoes and mash. Add the milk and cheese; set the mixture aside.
Preheat the oven to 375�F.
Brown the meat in a large skillet. Stir in the flour, and cook for 1 minute, stirring constantly. Add the vegetables and broth. Cook 5 minutes until bubbly.
Spoon the vegetable mixture into an 8-inch square baking dish. Spread the potato mixture over vegetable-meat mixture. Bake 25 minutes, until hot and bubbly.
