Heat gas or charcoal grill. In medium bowl, combine ground beef, salt and pepper; mix well. Shape mixture into 4 (1/2-inch-thick) patties.
When grill is heated, place patties on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook covered 11 to 13 minutes or until meat thermometer inserted in center of patties reads 160°F, turning once.
To toast rolls, during last 1 to 2 minutes of cooking time, place rolls, cut sides down, on grill.
Spread cut sides of rolls with mustard-mayonnaise sauce. Place patties on bottom halves of rolls. Top each with onion, tomato, cheese, basil and top half of roll.