Fill a large pot halfway with water. Add the cubed potatoes and cook at a gentle boil until tender, about 15 minutes.
Meanwhile, add the breadcrumbs and milk to a bowl and allow to soak until it turns into a paste.
Combine the ground beef with the paste and mix together thoroughly with your hands.
Form evenly sized meatballs, around 1 ¼ inch in diameter, compacting the meat into a sturdy ball.
Add the meatballs to a large skillet over medium-high heat. Allow them to brown on one side before turning them over. Attempt to evenly brown the balls on each side. This process takes about 10 minutes.
When finished, remove the meatballs from the pan. Add water to the pan and whisk in the brown gravy mix. Simmer until slightly thickened.
When the potatoes have finished cooking, drain the water. Mash the potatoes with a masher or hand mixer. Add butter and milk and stir well to combine.
Serve meatballs with mashed potatoes and gravy over top.