In a small bowl, combine tomatoes and water. Let stand for 5 minutes; drain. In a food processor, combine mayonnaise and tomatoes; cover and process until blended. Chill until serving., In a large bowl, combine the Worcestershire sauce, basil, Italian seasoning, garlic, pepper and salt. Crumble beef over mixture and mix well. Shape into 12 thin patties. Place 2 tablespoons cheese on six patties; top with remaining patties and press edges firmly to seal., On a greased grill, cook burgers, covered, over medium heat or broil 4 in. from the heat for 5-7 minutes on each side or until a thermometer reads 160° and juices run clear. Serve on buns with mayonnaise mixture and, if desired, additional basil.