Heat the oven to 375°F. Lightly grease 8 cups of a standard muffin pan.

Put the sweet potato chunks in a saucepan and cover them with water. Bring to a boil, then lower the heat and simmer until the potatoes are fork-tender, about 15 to 20 minutes.

While the sweet potatoes cook, combine the ground chicken, breadcrumbs, egg, Parmesan, onion, garlic powder, smoked paprika, kosher salt, black pepper, and 2 tablespoons of the barbecue sauce in a bowl. Mix gently until just combined.

Divide half of the chicken mixture among the 8 prepared muffin cups. Add a small pinch of mozzarella to the center of each portion, then cover with the remaining chicken mixture. Press gently around the cheese to seal it inside.

Brush the tops with the remaining barbecue sauce. Bake until the muffins are cooked through and reach 165°F in the center, about 20 to 25 minutes.

Drain the cooked sweet potatoes and return them to the saucepan. Add the butter, milk, and 1/4 teaspoon salt. Mash until smooth, adding a little more milk only if needed for your preferred texture.

Spoon the sweet potato mash onto plates and serve the chicken meatloaf muffins on top or alongside.