Combine salad ingredients in a large bowl; cover and refrigerate until ready to serve (up to 2 hours ahead).
For the vinaigrette, combine vinegar, garlic, salt, pepper, basil, sugar, mustard, olive oil and parmesan cheese in a blender. Puree until smooth.
Pour over salad greens and toss to coat or transfer undressed salad greens to a serving dish and add desired amount of dressing to individual salads. Garnish with additional Parmesan cheese if desired.