Step 1: Marinate the Chicken
In a medium bowl, whisk together 2 tablespoons of olive oil, minced parsley, fresh lemon juice, kosher salt, and black pepper. Add the chicken breasts and turn to coat evenly. Let the chicken marinate at room temperature for about 15 to 20 minutes while preparing the grill.
Step 2: Grill the Chicken
Preheat an outdoor grill to high heat or heat a grill pan over medium-high heat. Remove the chicken from the marinade and discard the remaining marinade.
Season both sides of the chicken with additional salt and pepper. Grill for 3 to 4 minutes per side until attractive grill marks develop. Reduce the heat or move the chicken to indirect heat, cover, and continue cooking until the internal temperature reaches 165°F (74°C).
Transfer the chicken to a cutting board and let it rest for 5 minutes before slicing into thin strips.
Step 3: Toast the Bread
Brush the cut sides of the sourdough bread with the remaining olive oil. Place the bread cut-side down on the grill or grill pan and toast until lightly golden and crisp.
Step 4: Assemble the Sandwiches
Slice the bread into individual sandwich portions.
Layer each piece with sliced grilled chicken, fresh mozzarella, and tomato slices.
Top with fresh basil leaves and drizzle generously with balsamic vinegar or balsamic glaze.
Finish with an extra drizzle of olive oil and season lightly with kosher salt and freshly ground black pepper.
Serve the Chicken Caprese Sandwich immediately while the bread is still warm and crisp.