Prepare the Vinaigrette: While the chicken is resting, whisk together the balsamic vinegar, olive oil, Dijon mustard, salt, and pepper in a small bowl until well combined. Set aside.
Assemble the Salad: In a large salad bowl, toss together the spring greens mix, chopped basil, halved cherry tomatoes, mozzarella, and the prepared vinaigrette.
Serve: Slice the rested chicken as desired and arrange it on top of the salad. Add the optional sliced avocado, any remaining fresh basil, and a sprinkle of freshly ground black pepper. The salad can be served with the chicken either warm or chilled, depending on your preference.