Heat the oven to 375°F. Line a rimmed baking sheet with parchment paper.

In a small bowl, stir together the breadcrumbs and 1/4 cup milk. Let them sit for a few minutes, until the breadcrumbs absorb the milk.

In a large bowl, combine the ground turkey, soaked breadcrumbs, egg, grated onion, garlic powder, smoked paprika, salt, and black pepper. Mix gently just until combined so the meatloaf stays tender.

Shape the mixture into a compact loaf on the prepared baking sheet. Spread 2 tablespoons of the barbecue sauce over the top. Bake until the center reaches 165°F, about 45 to 55 minutes. Brush the remaining barbecue sauce over the loaf during the last 10 minutes of baking.

While the meatloaf bakes, place the sweet potato chunks in a saucepan and cover them 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 the remaining 1/4 cup milk until smooth. Let the meatloaf rest for 5 minutes before slicing, then serve it over the mash.