I usually stuff them with cheese, a little seasoning on the outside (we like fennel seed on beef), and more cheese melted on the outside. Something it took me about 40 years to figure out: If you're making extras for leftovers to re-heat, don't melt cheese on them. It will disappear as you re-heat them. Instead, heat up the burger, then put fresh cheese on it.
I'm very intelligent, but I mask it by doing stupid stuff.