To make the secret sauce: In a small bowl, stir together the BBQ sauce, mustard, horseradish, ketchup, and mayonnaise. Season with pepper and then cover and chill until ready to use.
To make the burgers: Season the outsides liberally with salt and pepper. If using ground meat, gently form the chuck into 6 patties, about 1 inch thick.
Set a cast-iron skillet over medium-high heat and let heat for 1 minute. Add a drizzle of oil. As soon as the oil begins to smoke, add the burgers. Let cook undisturbed until well charred, 3-4 minutes. Flip and char the other sides, about 7 minutes total for medium-rare burgers.
To serve: Place the burgers on the English muffin bottoms and top each with some of the sauce and a tomato slice. Add the muffin tops and serve immediately.
