Marinate the chicken. Combine the balsamic vinegar, olive oil, and salt in a large resealable bag or a bowl. Add the chicken breasts and coat with the marinade. Allow to marinate for at least 15 minutes and up to 4 hours. If longer than 1 hour, marinate in the refrigerator.
Shake off excess marinade from the chicken and pat dry. Heat a 10-12” sauté pan to medium to medium high heat. Once the pan is hot, add oil to lightly coat the bottom of the pan. Add chicken and cook 5-6 minutes, then flip and cook on the other side until the internal temperature reaches 165ºF, ~5-6 more minutes.
Allow chicken to rest for 10 minutes, then cut into slices.
Build the sandwiches. Spread 1 Tablespoon pesto on each slice of bread. Top half of the bread slices with ~¼ cup arugula, 2 ounces of chicken, 1 ounce of mozzarella, 2 slices of tomato, and a drizzle of balsamic glaze. Place remaining bread slices on top.
Enjoy cold or warm. To toast the sandwich, brush a griddle or skillet with oil or butter. Add sandwich and cook until golden brown and toasty on one side, 2-3 minutes. Carefully flip and cook on the other side, 2-3 more minutes, or until bread is golden brown on both sides and mozzarella cheese is partially melted. Enjoy!