In a large bowl, whisk together balsamic vinegar, olive oil, garlic powder, dried basil, dried oregano, sea salt, and black pepper. Add the chicken breasts and turn to coat in the marinade. Set aside to marinate for at least 10 minutes, or marinate in the fridge for up to 8 hours.
Cook chicken breasts in the air fryer at 375°F (190°C) for 15-20 minutes, or in the oven at 400°F (200°C) for 20-25 minutes, or until internal temperature reaches 165°F (74°C).
Let the chicken rest for 5 minutes, then slice against the grain. Cover to keep warm.
Meanwhile, make the balsamic glaze by simmering 1/2 cup of balsamic vinegar in a small saucepan over medium-low heat until reduced by half and syrupy, about 10-15 minutes.
In a large salad bowl, combine lettuce, tomatoes, mozzarella balls, and chicken.
Sprinkle the salad with basil leaves and drizzle with balsamic glaze.