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 1/4 inch in diameter, compacting the meat into a sturdy ball.
Add the meatballs to a large skillet over medium-high heat. Don't crowd them or they won't get browned. Rotate and flip them until they are browned on all sides. 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, milk, and salt and stir well to combine.
Serve meatballs with mashed potatoes and gravy over top.