When I cook burgers for company - I will roll the patties out to half the normal thickness ( maybe...3/8" thick...?) and put a small dollop ( between a tsp. and a Tbls.) of a good pizza sauce - then a layer of pepperoni. Keep all of this approx. 1/2" away from the edges. Then lay another thin patty on top, and pinch the edges together to keep the stuff inside. When the patties are cooked, I throw a couple of slices of Mozzarella on top.
You can do similar using salsa verde, and some chorizo - and top 'em with Pepper Jack - or...whatever you like. Pimento cheese and jalapeño slices are a good combo stuffing too. The combinations are endless - just use your imagination!
It takes a little extra TLC on the grill when cooking them - easier on a flat top or cast iron smooth griddle - but what a fun surprise for your guests.
