Season the steaks with salt and pepper to taste. Place into a glass dish and drizzle with Worcestershire sauce. Turn the steaks, cover and refrigerate 15 minutes. Turn the steaks again and marinate 15 minutes longer.
Preheat an outdoor barbecue for medium-high heat and lightly oil the cooking grate.
Place the steaks on the preheated barbecue, close lid and cook for 7 minutes. Toss the asparagus spears with a little olive oil and season with salt and pepper to taste. Place the asparagus onto the barbecue, turn steaks over and close lid. Cook until the steaks are beginning to firm and are slightly pink in the centre and the asparagus is tender, about 7 additional minutes. Turn the asparagus halfway through. Top each steak with 3 asparagus spears and a slice of Gruyere. Continue cooking until the cheese has melted. Remove from the barbecue and let stand 5 minutes before serving.