Fennel gives this salad its signature crunch and lends a sweetness to balance the red onions and parsley.
Prepare a large ice-water bath. Put parsley, fennel, and onion in a colander, and set in ice-water bath. Let soak 10 minutes.
Drain, and transfer to a salad spinner. Spin until dry, and transfer to a serving bowl. Add lemon juice, oil, and celery seeds; toss to combine. Season with salt and pepper.
Soaking the components of this simple salad in ice water for 10 minutes makes them cool and crisp. It also helps mellow the flavor of the red onions.