In a small bowl, whisk together balsamic vinegar, olive oil, brown sugar, minced garlic, dried basil, and salt until smooth and emulsified.

Place chicken thighs in shallow dish, pour 4 tablespoons of prepared dressing over chicken, cover, and marinate for at least 30 minutes in refrigerator.

Heat olive oil in grill pan over medium-high heat; grill marinated chicken for about 5 minutes on each side until golden brown and cooked through.

Transfer cooked chicken to cutting board, let rest for about 5 minutes, then slice into strips.

In large mixing bowl, combine chopped romaine, sliced avocado, halved cherry tomatoes, and mozzarella balls. Arrange grilled chicken on top.

Drizzle reserved dressing over salad, add fresh basil leaves, and toss gently to combine all ingredients.

Serve in individual bowls or a large platter, garnishing with additional basil leaves as desired.