Preheat grill to medium then line with non-stick foil.
Stir the minced garlic, salt and pepper into the butter. Brush onion slices evenly with garlic-butter mixture as they are placed on grill. Close the lid and cook, turning and moving as needed, for 20 minutes. Increase heat to medium-high.
Lay flattened breasts on the grill grates. With the remaining garlic sauce, brush all over chicken. Grill, turning once, for 10-12 minutes or until cooked through coating with barbecue sauce in the last few minutes.
Top each piece of chicken with onions and one slice cheese. Cover and let stand for 30 seconds. Toast buns on grill and spread with mayonnaise or barbecue sauce. Top with chicken steaks and two slices bacon. Close with bread top.