Heat the oven to 375°F. Lightly grease an 8-cup muffin pan.
Add the potatoes to a pot and cover them with water. Bring to a boil, then cook until the potatoes are fork-tender, about 15 to 20 minutes. Drain and return them to the pot.
While the potatoes cook, combine the ground turkey, breadcrumbs, egg, diced onion, 1/4 cup milk, garlic powder, salt, black pepper, and 1/4 cup of the BBQ sauce in a mixing bowl. Mix gently until just combined.
Divide the turkey mixture among the prepared muffin cups, filling each cup evenly. Spoon the remaining 1/4 cup BBQ sauce over the tops.
Bake until the muffins are cooked through and reach 165°F in the center, about 20 to 25 minutes. Let them rest in the pan for 5 minutes before removing.
Mash the drained potatoes with the butter and remaining 1/3 cup milk until smooth. Serve the BBQ-glazed meatloaf muffins with the mashed potatoes.