Sprinkle the ground beef evenly with 1/2 teaspoon salt in a large bowl. Gently form the meat into 4 balls, then lightly press into 4-inch-wide, 1-inch-thick patties. Make a 2-inch-wide indentation in the center of each with your thumb to prevent the burgers from bulging when grilled.
Preheat a grill to high. Season the patties with salt and pepper. Grill, undisturbed, until marked on the bottom, 3 to 5 minutes. Turn and grill until the other side is marked and the patties feel firm, 3 to 5 more minutes; if desired, top each burger with 2 slices cheese during the last 2 minutes of cooking and cover with a disposable aluminum pan to melt.
Serve the patties on the buns; top with lettuce and tomato.