Heat grill to medium. Arrange 4 of the tortillas on a cutting board. Arrange the mozzarella and tomatoes on the tortillas, leaving a 1-inch border empty. Season with 1/2 teaspoon of the salt and the pepper and top with the remaining tortillas. In a medium bowl, combine the basil, pine nuts, oil, and the remaining salt; set aside. Cook the quesadillas around the perimeter of the grill until the cheese melts and the tortillas are crisp and golden, about 2 minutes per side. Immediately cut the quesadillas into wedges and serve with the basil salad.
Tip: Instead of grilling the quesadillas, try broiling them. Arrange them on a baking sheet and broil, turning once, until the cheese melts and the tortillas are golden brown.