In a large bowl, mix the chopped celery and leaves (or parsley), chopped apple, chopped dates, sliced radishes, roasted nuts, and parmesan cheese. Toss well to combine, unsticking the dates from each other.
Squeeze fresh lemon juice over the top of the salad, using one or both lemon halves, to taste. Careful to remove any seeds.
Drizzle with olive oil, and add a couple healthy pinches of flaky sea salt. Mix the salad well, and taste. Adjust lemon juice and salt as needed.
Serve immediately. Salad keeps very well in the fridge for up to three days.