In a large bowl, combine the Worcestershire sauce, tomato paste, horseradish, parsley and lemon juice, if using. Add the meat, pepper, kosher salt and celery salt. Using your hands, mix to combine. Form into 12 slider-size patties (thinner at the center for even cooking).
In a medium size bowl, mix the ketchup, HP sauce, celery and Tabasco to make the crunchy ketchup.
In a cast iron skillet, heat the EVOO over medium-high. Cook the patties, turning once, for about 8 minutes for medium-rare doneness. Divide the patties among the roll bottoms. Top with the lettuce, tomato, onion, crunchy ketchup and roll tops. Garnish the burgers with olives and onions, if using, skewered on toothpicks.