For the dressing, combine the garlic, oil, vinegar, egg yolk, sugar, mustard, and a generous pinch of salt and pepper in a blender, and process until creamy and smooth, 30 to 60 seconds.
For the salad, combine the chicken, bacon, salami, tomatoes, lettuce, onion, banana peppers, garbanzo beans, mozzarella, and Parmesan in a large bowl.
Season with salt and pepper and gently toss until mixed.
Add enough dressing to lightly coat.
Taste and add more dressing, salt, and pepper if desired.
