Heat the oven to 375°F. Lightly grease 8 cups of a standard muffin pan.
Put the potatoes in a saucepan and cover them with water. Bring to a boil, then cook until the potatoes are fork-tender, about 15 minutes. Drain well and return them to the pan.
Mash the potatoes with the butter, warm milk, and 1/4 teaspoon salt until smooth. Set aside while you prepare the meat mixture.
In a large bowl, combine the breadcrumbs and 1/4 cup milk. Let them stand for 2 minutes. Add the ground beef, egg, onion, Worcestershire sauce, garlic powder, salt, and black pepper. Mix gently until just combined.
Divide the beef mixture among the 8 greased muffin cups. Press it into the bottoms and up the sides of each cup, leaving a hollow in the center. Spoon mashed potatoes into each hollow.
Spread the remaining ketchup over the exposed meat around the potato centers. Bake for 25 to 30 minutes, until the beef is cooked through.
Let the muffins rest in the pan for 5 minutes. Carefully loosen the edges with a spoon and lift them out to serve.