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Brown the ground beef with the onions and garlic. Drain any accumulated fat. Rinse with hot water for extra fat-leaching or blot with a paper towel. Stir in the vegetables and seasonings (up to the sour cream) and cook a few more minutes to blend. Turn the heat off and stir in the sour cream.
Put the meat and vegetable mixture into a 9x9 pan. Spread the mashed potatoes over the top, then sprinkle the grated cheese on top of the potatoes. Sprinkle some paprika across the cheese.
Bake at 350 for 20-30 minutes until heated through. Likewise, if your skillet is oven-proof you could just put the potatoes on top of the meat, top with the potatoes and cheese, and then put the whole skillet in the oven rather than dirtying another dish.