Cut onion in half then each half into thin slices OR, chop the onion. Melt butter in a large skillet or pot over medium heat then add onions and a dash of salt. Cook, stirring every couple of minutes, until onions are golden brown and caramelized, about 20 minutes. Turn heat down if onions start to burn. Set aside to cool slightly - can be made up to several days ahead of time.
Preheat oven to 425 degrees. In a large bowl combine ground beef, egg, Worcestershire sauce, 2 Tablespoons BBQ sauce, bread crumbs, salt, pepper, cheese cubes, and caramelized onions, then mix until just combined. Divide mixture into 4 equal-sized portions then form into loaves and place on a foil-lined, non-stick-sprayed baking sheet. Spread 1 Tablespoon BBQ sauce over each loaf then bake for 20 minutes, or until no longer pink in the center, and then serve.