Place the beef in a mixing bowl; season liberally with kosher salt and lots of black pepper. Add the Worcestershire sauce, horseradish, Tabasco, celery tops and leaves, ketchup or chili sauce, cracker crumbs and egg yolk. Combine and form four large patties that are thinner at the center than the edges for even cooking.
Combine the sauce ingredients in a small bowl.
Heat cast iron skillet or griddle pan over medium-high heat. Add EVOO and wipe around pan – it will smoke up a bit. Add the burgers and cook for 8-10 minutes, turning once. Top with the cheese in last minute or two of cooking time.
Serve on brioche rolls topped with the special sauce.