16 thin slices whole-milk mozzarella (from a 1-lb block; not fresh)
Directions
Heat 2 tablespoons oil in a 12-inch heavy skillet over moderate heat until hot but not smoking, then cook garlic and red-pepper flakes, stirring, 30 seconds. Add tomatoes and salt and cook, stirring, until thickened, about 6 minutes. Remove from heat and stir in basil and parmesan.
Prepare a gas grill for direct-heat cooking over moderate heat.
Trim 1/4 inch off 2 opposite long sides of each eggplant. Cut each eggplant lengthwise (in same direction as trimmed sides so each slice has skin just around edge) into 4 slices. Brush slices with remaining 2 tablespoons oil.
Grill eggplant, covered, turning over once, until tender, about 6 minutes total. Transfer to a work surface.
Spread top of each slice with about 1 tablespoon tomato sauce and top with a slice of mozzarella, then restack each eggplant. Transfer stacks to a shallow baking pan and grill, covered, just until cheese is melted, about 4 minutes.
