In a small bowl, whisk together the garlic, lemon juice, mustard, anchovy paste, grated Parmesan, oil, and a few grinds of pepper. Set aside.
Place half a romaine heart on each plate and top with some of the chicken, chickpeas, avocado, and walnuts. Drizzle with the dressing.
Use a vegetable peeler to create long Parmesan shavings for the topping, if desired.