Peel the potatoes, cutting them into fourths, put them in enough water that they are covered and bring to a boil.
While they are cooking, start putting together the meat mixture. Mix together the ground beef, 1/2 chopped onion, garlic, egg, and bread crumbs. Press the meat mixture into an 8-inch pie pan and shape the edges as you would a pie shell.
Preheat oven to 350 degrees F. When the potatoes are fork tender, drain them and mash them. Add the butter. Add enough milk to moisten the potatoes, not too moist. The cheese will make them the right texture. Add salt and pepper. Melt the Velveeta and add this to the potatoes and add the remaining half of the onions. Mix thoroughly. Pile the potato mixture on top of the ground beef in the pie pan.
Put in the oven for 1 hour, or until the meat is done. The potatoes on top will be golden brown. Let cool for a few minutes. Cut in wedges just like you would cut a pie.