In a mixing bowl, combine olive oil, minced garlic, dried thyme, dried rosemary, salt, and pepper to create the marinade.
Place the London broil steak in a shallow dish or resealable plastic bag and pour the marinade over the steak, ensuring it is well coated. Marinate in the refrigerator for at least 30 minutes, or up to 4 hours for maximum flavor.
Preheat the grill or grill pan over medium-high heat. Remove the steak from the marinade and discard any excess marinade.
Grill the steak for 5-7 minutes per side, or until it reaches your desired level of doneness. Use a meat thermometer to check for an internal temperature of 135°F (for medium-rare), 145°F (for medium), or 160°F (for well-done).
Once cooked to your preference, transfer the steak to a cutting board and let it rest for 5 minutes before slicing thinly against the grain.
While the steak is resting, heat a skillet or sauté pan over medium heat. Add a drizzle of olive oil and the thinly sliced onions. Cook, stirring occasionally, until the onions are caramelized and golden brown, about 10-15 minutes.
Slice the sandwich rolls or baguettes in half and lightly toast them on the grill or in the oven.
To assemble the sandwiches, place slices of grilled steak on the bottom halves of the rolls. Top with caramelized onions and a slice of cheese.
Place the sandwiches under the broiler for 1-2 minutes, or until the cheese is melted and bubbly.
Remove from the broiler and top with optional toppings such as lettuce, tomato, avocado, mayonnaise, or mustard, if desired.
Serve the London Broil Steak Sandwiches immediately and enjoy!