Soak 4 wooden skewers in water. Preheat a grill to medium. Lay the steak flat on a work surface and season with salt and pepper. Split the roasted peppers and lay flat on the meat, leaving a 1-inch border at both short ends. Layer the basil and mozzarella on top; season with salt and pepper. Roll up the steak, beginning with a short end, and secure with the skewers, pushed all the way through and evenly spaced apart. Cut the roll crosswise, between the skewers, into 4 equal pinwheels. Lay each one flat.
Drizzle the cut sides of each pinwheel with the olive oil; season with salt and pepper.
Grill, covered, turning once, for about 6 minutes.
