Rinse all of the vegetables well; chop off the tough ends of the asparagus and discard.
Run a vegetable peeler, or potato peeler, down the full length of each stalk of asparagus, adding the shavings to a large salad bowl.
Once down to the center of the asparagus and it becomes difficult to peel, chop the remaining parts finely and add to the salad.
Thinly slice the radishes and fennel bulb; add to the salad bowl along with the chopped walnuts and feta cheese.
Pour all of the lemon-parsley dressing over the salad and toss well.
If desired, serve the salad with chopped hard boiled eggs and avocado.