Heat a cast-iron skillet over medium-high heat.
Place meat in bowl and season with salt and pepper. Add onion, garlic, Worcestershire, Dijon, hot sauce, relish, celery seed, paprika and parsley, and mix well. Form 4 patties and drizzle with oil.
Cook patties 8 minutes in the hot pan, turning once. Top with cheese the last minute to melt. Serve on rolls with lettuce, tomato and onion.