Prepare the London Broil: Begin by setting a large resealable plastic bag in a medium saucepan, folding the edges over the sides to keep the bag stable. In the bag, combine the olive oil, Worcestershire sauce, smashed garlic cloves, lemon juice, kosher salt, and freshly ground black pepper. Whisk to blend the ingredients thoroughly. Add the London broil to the bag and seal it tightly. Gently rotate the bag to ensure the meat is evenly coated with the marinade. Lay the bag flat on a cutting board and allow it to marinate at room temperature for about one hour, flipping the bag halfway through the time. Alternatively, marinate the steak in the refrigerator overnight, and let it rest at room temperature for 20 minutes before cooking.
Prepare the Gribiche: While the steak marinates, fill a medium saucepan with water and bring it to a boil over high heat. Use a spoon to gently lower the eggs into the water, and let them boil for 10 minutes. After boiling, drain the eggs and rinse them under cold water to stop the cooking process. Once cool, peel and roughly chop the eggs. In a medium bowl, whisk together the extra-virgin olive oil, Dijon mustard, white wine vinegar, grated garlic, and a pinch of salt and pepper. Stir in the chopped parsley, dried chives, capers, and cornichons. Carefully fold in the chopped eggs and cover the mixture to marinate. This gribiche can be made ahead of time and stored in the refrigerator for up to two days—just be sure to return it to room temperature before serving.
Broil the London Broil: Position an oven rack approximately 4 inches from the broiler's heating element and preheat the broiler to high. Line a rimmed baking sheet with aluminum foil and place it in the oven to preheat. Remove the marinated steak from the bag, discarding any garlic cloves that may have stuck to the meat. Transfer the preheated baking sheet to the oven and place the steak in the center. Broil for about 6 to 10 minutes, depending on the thickness of the steak, until the exterior is nicely charred, and an instant-read thermometer inserted sideways into the center of the steak registers between 120°F and 125°F for a medium-rare finish. Once broiled, transfer the steak to a cutting board and allow it to rest for 10 minutes.
Prepare the Asparagus: While the steak rests, add the asparagus to the same preheated sheet pan. Drizzle the asparagus with olive oil, and season it with kosher salt and freshly ground black pepper. Broil for approximately 3 minutes, or until the asparagus is bright green and crisp-tender.
Assemble and Serve: Slice the rested steak against the grain and arrange it on serving plates. Divide the broiled asparagus between the plates, and generously spoon the gribiche dressing over the top of the vegetables and steak. Serve immediately and enjoy this elevated sheet pan dinner.