Preheat grill to medium-high heat.
Slice chicken breasts in half horizontally so you have thinner pieces. Season with salt, pepper, and garlic powder. Grill chicken until internal temperature reaches 165 degrees. In the last few minutes of cooking chicken, place a slice of fresh mozzarella on top.
Lightly brush the inside of the ciabatta rolls with olive oil. Place rolls with oil side down on hot grill and cook just until toasted.
Meanwhile make the pesto. Wash and dry basil thoroughly. Place basil, pine nuts, chopped garlic, and salt in the work bowl of a food processor. Process quickly to make a coarse paste. With the motor running add the olive oil, and process for another 5 seconds. Place pesto in a bowl and mix in the parmesan cheese.
Spread a generous amount of pesto on the rolls. Assemble sandwiches by placing chicken breast on bottom bun, then tomato, and lastly arugula.