In a mixing bowl, whisk together balsamic vinegar, extra-virgin olive oil, Dijon mustard, honey, minced garlic, salt, and pepper until smooth. Add the thinly sliced chicken breast, ensuring it's well-coated. Let marinate for about 10-12 minutes.

While the chicken marinates, heat a skillet over medium heat. Brush both halves of the rolls with olive oil and toast for about 2-3 minutes until golden brown.

Once toasted, layer provolone and mozzarella cheese on the bottom half of each roll, add the marinated chicken, and sprinkle with fresh herbs.

Close each sandwich with the top half of the roll. Grill in the skillet for 2-3 minutes, covered, until the cheese is melted and the bread is golden.

Let the sandwiches rest for 1-2 minutes before slicing diagonally. Drizzle with balsamic reduction if desired.