Place the tomatoes in a small bowl and pour the boiling water over them. Let sit for 5 minutes and then drain. Combine drained tomatoes and mayonnaise in a food processor and pulse until blended. Scoop into a bowl and refrigerate until serving.

Place the Worcestershire sauce, basil, Italian seasoning, garlic, pepper, salt and ground beef in a large bowl and combine thoroughly. Separate and form the meat mixture into 12 thin patties. In the center of 6 of the patties, place 1 tablespoon of mozzarella cheese. Cover the cheese with the six remaining patties and squeeze the edges together to seal, forming one larger patty with cheese in the center.

Grill burgers, covered, over medium heat on a grill or broil 4 inches from the heat for 5-7 minutes on each side or until cooked through. Place each burger on a bun, spread the mayonnaise evenly over the burgers and top with additional basil leaves as desired.