Heat the oven to 375°F. Lightly grease a 12-cup muffin pan.
Add the ground turkey, egg, breadcrumbs, onion, 2 tablespoons of the barbecue sauce, Worcestershire sauce, garlic powder, smoked paprika, salt, and black pepper to a mixing bowl. Mix gently until combined, taking care not to compact the turkey.
Divide the mixture among 8 muffin cups, filling each cup evenly. Spoon the remaining barbecue sauce over the tops.
Bake for 20 to 25 minutes, until the muffins are cooked through and the centers reach 165°F. Let them rest in the pan for 5 minutes before removing.
While the muffins bake, place the sweet potato chunks in a saucepan and cover with water. Bring to a boil, then reduce the heat and simmer until the potatoes are very tender, about 15 to 20 minutes. Drain well.
Mash the sweet potatoes with the butter and milk until smooth. Serve each turkey meatloaf muffin with a scoop of sweet potato mash.