LOL. Funny story, I actually made a new specialty messing around in the kitchen this way. Same scenario...was making bacon cheeseburgers, but had no buns...
But I did have bagels...
Then it dawned on me...

BAGEL BURGERS!
It worked out perfectly. Over time I learned how to perfect my method. I used those thomas english muffin square bagels that have more surface area on the bagel and the hole is smaller. As well, I would experiment with different types of those bagels.
It wasn't an idea unique to me as I found out later...but damn, when I made that discovery I felt like I was truly onto something.