Brown ground beef in a skillet or dutch oven. Drain.
Stir the onion and garlic with the beef and continue to saute until the onion is transparent, about 5-6 minutes.
Stir in the flour, worcestershire sauce, paprika, salt, black pepper, tomato paste, beef broth, and frozen mixed vegetables. Bring to a boil, then lower heat to a simmer for about 15-20 minutes so that the gravy thickens slightly.
While you are preparing the meat mixture, make the mashed potatoes in a separate pot. Bring the potatoes to a boil until tender. Drain the water from the pot. Add the butter and milk to the potatoes and mash with a potato masher until smooth.
Spread the meat mixture in a rectangular baking dish. Spread the mashed potatoes on top of the meat mixture. Sprinkle grated cheese on top.
Bake in a 350F oven for 45 minutes or until the cheese is melted and the shepherd's pie is bubbly around the edges.