I have done these a number of ways, usually with fresh onion, mayo, pineapple slice and Teriyaki sauce, but today did a different method.
In a 4oz bowl I combined BBQ sauce (Stubb’s original), with a splash of soy sauce, brown sugar, and thin chunks of fresh pineapple.
I then caramelized thinly sliced white onions with julienned green bell pepper in butter, and when seriously browned, added the above sauce/fruit and reduced until thickened.
Burger was pan fried with cheese added after seasoning/turning, and placed cheese side down on bottom of toasted bun. The thickened BBQ/onion/pepper/pineapple sauce was then added to the top of the burger, covered with the top of the toasted bun.
OMG, seriously yum!