Place cubed potatoes and garlic in a large pot with enough water to cover. Bring to a boil over high heat; reduce heat to medium-low, cover, and simmer until tender, about 20 minutes.
Preheat the oven to 375 degrees F (190 degrees C).
Brown ground beef over medium heat in a skillet. Stir in flour, mixing with beef drippings.
Add beef broth, ketchup and vegetables. Stir to combine. Cook for 5 minutes, until thick.
Transfer beef mixture into an oven-proof casserole dish.
Drain potatoes and smash them a little bit before adding 1/4 cup of grated cheese and sour cream. Mash together until smooth.
Spoon potatoes onto the middle of the meat mixture. With a fork, spread potatoes from the center to the edges to form the top layer.
Sprinkle with remaining 1/4 cup of grated cheese.
Bake in the preheated oven for 20-25 minutes, or until cheese is melted and golden. Let cool 15 minutes before serving.
