Form the ground beef into 4 patties that are no more than ¾ of an inch thick. Make a depression in the center of each patty. Season on both sides with salt and pepper.
In a medium bowl combine avocados, onion, jalapeno pepper, and cilantro. Add lime juice and season with salt and pepper. Mash briefly with a fork until a salsa has formed.
Lightly grease the grates of an outdoor grill. Heat the grill to medium-high heat. Add the burgers and cook, turning once until fully cooked (the internal temperature has reached 160 degrees F.). During the last minute of cooking top each burger with a slice of cheese. Cook until cheese has melted.
Split the hamburger buns and place cutside down onto the grill until lightly toasted. Top the bottom half of each bun with 1 piece of romaine, 1 slice of tomato, 1 hamburger patty, avocado salsa, and the top bun.