Heat the oven to 375°F. Lightly grease 8 cups of a standard muffin pan.
In a large bowl, gently combine the ground turkey, egg, breadcrumbs, diced onion, 2 tablespoons milk, garlic powder, smoked paprika, salt, black pepper, and 2 tablespoons of the BBQ sauce. Stop mixing as soon as the ingredients are evenly combined.
Divide the turkey mixture among the 8 prepared muffin cups. Bake for 20 minutes.
Remove the pan from the oven and brush the tops of the muffins with the remaining BBQ sauce. Return them to the oven and bake for 5 to 10 minutes, until cooked through. Let them rest briefly before removing from the pan.
While the muffins bake, place the sweet potato chunks in a saucepan and cover them with water. Bring to a boil, then simmer until very tender, about 15 to 20 minutes. Drain well.
Mash the sweet potatoes with the butter and ¼ cup milk until smooth. Spoon the mash onto plates and serve the BBQ turkey meatloaf muffins on top or alongside.