Pesto Chicken Sandwiches

Season the chicken breast halves with salt and pepper and sprinkle evenly with the Italian seasoning. Brush lightly on all sides with the oil. Prepare a charcoal or gas grill for direct grilling over high heat. Brush and oil the grill grate. Place the chicken on the grill directly over the fire and cook until nicely grill-marked and relatively firm to the touch, 5 to 8 minutes on each side depending on the thickness. You want the chicken to be opaque throughout but still moist and juicy inside. About 2 minutes before the chicken is ready, place 2 slices of the cheese on each breast half, cover the grill and allow the cheese to melt. Put the bread slices along the edge of the grill at the same time, and turn once after 1 minute to toast both sides. Transfer the chicken and bread slices to a cutting board. Spread the bread slices with mayonnaise, if desired. Cut each breast half against the grain on the diagonal into 3 to 4 pieces. Arrange one sliced breast half on each of 4 bread slices. Top with 2 tomato slices, and then top the tomatoes with 1 tablespoon of the pesto, spreading it evenly over the tomatoes. Close the sandwiches with the remaining bread slices, and serve.