Cut the red potatoes into 1-inch chunks and bring them to a boil in salted water along with the minced garlic cloves. Cook for approximately 20 minutes until the potatoes are completely fork-tender, then drain well in a colander. Return the drained potatoes and garlic to the pot, add the sour cream and 1/4 cup of the shredded cheddar cheese, then mash until you reach your desired consistency—I prefer leaving it slightly chunky rather than completely smooth for better texture. Set aside and preheat your oven to 375°F while you prepare the beef filling.
In a large skillet over medium-high heat, cook the ground beef, breaking it apart with a spoon as it browns, until no pink remains (about 5-7 minutes). Once cooked through, sprinkle the flour over the beef and stir constantly for 1 minute—this helps thicken the sauce and adds body to the filling. I like to use a whisk here to break up any lumps and ensure the flour is fully incorporated and coats the meat evenly.
Pour the beef broth into the skillet with the cooked beef, then add the frozen mixed vegetables and ketchup. Stir well to combine all ingredients, then simmer over medium heat for 5 minutes, allowing the flavors to meld and the vegetables to warm through. The broth will create a savory sauce that keeps the filling moist during baking.
Transfer the beef and vegetable mixture from Step 3 into a 9x13-inch baking dish, spreading it in an even layer. Top with the potato mixture from Step 1, spreading it evenly across the surface to seal in the filling. Bake at 375°F for 18 minutes until the filling is bubbling at the edges and the potatoes begin to golden slightly.
Remove the baking dish from the oven and immediately sprinkle the remaining 1/4 cup of shredded cheddar cheese evenly over the top. Return to the oven and bake for just 2 more minutes until the cheese is completely melted and slightly bubbly. Let rest for 2-3 minutes before serving—this helps the filling set slightly and makes serving cleaner. I always top with the cheese at the very end because it gives you that nice melted, slightly browned cheese layer without it getting lost in the longer bake.