What about brie especially when it's ripe and especially when placed below the burger, Gouda (esp well aged gouda that's room temp or higher and sweating) and p

What about brie especially when it's ripe and especially when placed below the burger, Gouda (esp well aged gouda that's room temp or higher and sweating) and pretty much anything made by Sartori work amazingly well on burgers. Goat cheese too. And cultured butters that are very close to cream consistency, like what Benedikt Dairy makes in New Hampshire (I'm sure there are comparable ones all over the USA?) can be even better. I'd never put processed cheese on a burger...