This is really spectacularly good. It's the filet mignon steak sandwich at 44 & X, and it's what I ate yesterday for lunch.
If you make one at home (recommended! only a few weeks of summer grilling opportunities left!), choose the meat according to your preference (filet mignon = tender and fancy; shell steak = chewier and less pricey), and definitely serve it on a very fluffy bun with caramelized onions, sauteed spinach, and maybe some cheese and mushrooms, for bonus points.