Place beef in mixing bowl, season liberally with kosher salt and lots of black pepper. Add Worcestershire, horseradish, Tabasco, celery tops and leaves, ketchup or chili sauce, cracker crumbs and egg yolk. Combine and form 4 large patties that are thinner at the center than the edges for even cooking.
Combine sauce ingredients in small bowl.
Heat cast-iron skillet or griddle pan over medium-high heat. Add oil and wipe around pan -- it will smoke up a bit. Add burgers and cook 8-10 minutes, turning once. Top with cheese in last minute or 2 of your cooking time. Serve on brioche rolls topped with special sauce.