Heat the oven to 375°F. Line a small baking sheet with parchment paper. Place the sweet potato chunks in a saucepan, cover with water, and bring to a boil.
While the sweet potatoes cook, combine the ground turkey, egg, breadcrumbs, diced onion, garlic powder, smoked paprika, salt, black pepper, and 2 tablespoons of the BBQ sauce in a mixing bowl. Mix just until combined.
Shape the turkey mixture into a compact loaf on the prepared baking sheet. Spread the remaining BBQ sauce over the top.
Bake for 40 to 45 minutes, until the center reaches 165°F. Let the meatloaf rest for 5 minutes before slicing.
Simmer the sweet potatoes until very tender, about 15 to 20 minutes. Drain well, then mash with the butter and milk until smooth. Serve with slices of BBQ turkey meatloaf.