Celery is the star ingredient in this tasty and unusual salad. It provides a great crunch, and its clean, grassy flavor is highlighted by a light and fresh-tasting lemon vinaigrette. The combination of buttery avocado, peppery arugula, mellow walnuts, and salty cheese is a winner!
Place the oil, lemon juice, shallots, and salt and pepper to taste in a small jar and seal the lid tightly. Shake vigorously to emulsify the dressing. Set aside at room temperature.
Place the celery in a small bowl and add 2 tablespoons of the dressing, stirring to coat the slices. Place the arugula in a salad bowl and add about 1 tablespoon of the dressing, tossing to coat; use more dressing as needed.
Divide the greens among 4 salad plates. Top each of the salads with some of the avocado and celery slices. Sprinkle with the walnuts, plus salt and freshly ground black pepper as desired. Using a vegetable peeler, shave a few thin slices of cheese over each salad. Serve immediately.