The Selective Spud

looking over the menu with disdain Ah, a fast food aficionado such as yourself should be able to cater to my culinary conundrum. I require a burger that defies the very laws of gastronomy: half the bun must be toasted, the other half not; the patty must be both rare and well-done, the cheese melted and cold simultaneously. Can you handle such a paradoxical request?