Heat the oven to 375°F. Lightly grease eight cups of a standard muffin tin.
Add the ground turkey, breadcrumbs, egg, diced onion, 2 tablespoons of the barbecue sauce, Worcestershire sauce, garlic powder, smoked paprika, salt, and black pepper to a bowl. Mix gently until just combined.
Divide the turkey mixture among the eight prepared muffin cups. Shape each portion loosely, then spread the remaining barbecue sauce over the tops.
Bake for 20 to 25 minutes, until the muffins are cooked through and reach 165°F in the center.
While the muffins bake, put the sweet potato chunks in a saucepan and cover them with water. Bring to a boil, then simmer until fork-tender, about 15 to 20 minutes. Drain well.
Return the sweet potatoes to the saucepan. Add the butter and milk, then mash until smooth. Serve the mash with the barbecue turkey muffins.