Balsamic Glaze: In a sauce pan, add all of the ingredients and whisk together. Bring to a rolling boil and boil until the sauce begins to thicken. Once the sauce is thick enough to drizzle, remove from the heat and set aside. The sauce will thicken as it sits and cools. Keep the glaze in your fridge for up to 30 days. Serve on salads, over pastas or on sandwiches.
Sandwiches: For the chicken marinade, combine all of the ingredients together in a ziploc bag or Tupperware and add the chicken into it. Toss to coat the chicken and keep in the fridge until ready to serve.
When ready to cook the chicken, heat an outdoor grill to medium-high heat. Place the chicken on the grill and cook on both sides until the center is no longer pink (time will depend how thick your pieces of chicken are). Once the chicken is cooked, remove from the grill and set aside.
Slice the tomatoes, red onion and lettuce for the sandwiches. Cut the buns in half and spread a generous portion of the mayo and pesto onto both sides of the bun. Place a piece of chicken on the bun, along with the garnishing of your choice. Serve the sandwiches with a drizzle of balsamic glaze if you wish.