Heat the oven to 375°F. Lightly grease 8 cups of a standard muffin pan.

Put the potato chunks in a saucepan and cover them with water. Add 1/4 teaspoon of the salt. Bring to a boil, then simmer until the potatoes are tender when pierced with a fork, about 15 to 20 minutes.

While the potatoes cook, combine the ground beef, stuffing mix, egg, 1/4 cup milk, onion, garlic powder, black pepper, and remaining 1/4 teaspoon salt in a bowl. Mix gently just until combined.

Divide the meat mixture among the 8 prepared muffin cups. Press a small well into the center of each portion. Place one cheddar cube in each well, then cover the cheese with the meat mixture and gently seal the tops.

Brush the tops with half of the barbecue sauce. Bake until the meat is cooked through, about 20 to 25 minutes. Spoon the remaining barbecue sauce over the muffins during the last 5 minutes of baking.

Drain the cooked potatoes and return them to the saucepan. Add the butter and 1/4 cup milk for the potatoes. Mash until creamy, then serve alongside the meatloaf muffins.