Prep the chicken:
Cut the chicken breasts in half lengthwise, creating 4 thin filets. Sandwich a piece between two pieces of parchment paper or plastic wrap. Use a meat mallet or rolling pin to beat it to an even 1/4-inch thickness. Repeat with the remaining 3 filets.
Marinate the chicken:
In a shallow dish, whisk together the olive oil, Italian seasoning, salt, and pepper. Place the chicken in the dish and turn to coat. Cover with plastic wrap and transfer to the fridge to marinate for at least 30 minutes or up to 8 hours.
Grill the chicken and toast the buns:
Preheat your grill to medium-high heat and lightly oil the grates.
Remove the chicken from the marinade and place it on the grill. Cook on one side for 3 minutes, then flip and cook on the other side for 3 minutes. Try not to move the chicken while it cooks except for flipping once. The chicken should be cooked through, golden with grill marks, and the internal temperature should be 165°F. Transfer the chicken to a plate and let it rest for 5 minutes.
While the chicken is grilling, you can also toast the rolls by placing them cut-side down on the grill for 1 to 2 minutes.
Assemble the sandwich:
Spread a generous layer of pesto on the bottom half of each ciabatta roll (about a tablespoon per roll). Add a layer of mozzarella slices, then a layer of tomato slices. Place a piece of grilled chicken on each sandwich. Finish off the sandwich with 5 to 6 fresh basil leaves and a drizzle of balsamic glaze, if desired. Place the other half of the roll on top.
This sandwich is best if you eat it fresh off the grill. Store any leftover chicken in an airtight container for up to 3 days. Store the tomatoes and mozzarella in a separate container. To reheat the chicken, place it in the oven at 400°F for 10 minutes, then assemble your sandwich.