Heat the oven to 375°F. Lightly grease a 12-cup muffin pan.
In a large bowl, combine the ground chicken, one egg, breadcrumbs, 2 tablespoons of the barbecue sauce, cheddar, onion powder, garlic powder, and 1/4 teaspoon salt. Mix gently until combined.
Divide the chicken mixture evenly among 8 muffin cups. Press it into the cups without packing it too firmly. Brush the tops with the remaining barbecue sauce.
In a separate bowl, whisk together the cornmeal, flour, sugar, baking powder, and remaining 1/4 teaspoon salt. In another bowl, whisk the second egg with the milk and melted butter. Stir the wet mixture into the dry ingredients just until no dry patches remain.
Spoon the cornbread batter over the chicken mixture, dividing it evenly among the filled cups. Leave a little room at the top for the batter to rise.
Bake until the cornbread tops are golden and the chicken is cooked through, about 25 to 30 minutes. The center of a muffin should reach 165°F on an instant-read thermometer.
Let the muffins rest in the pan for 5 minutes, then loosen the edges and lift them out. Serve warm.