Make the salad
To prepare the vegetables, bring a large saucepan filled with 4 quarts water and the kosher salt to a boil.
Meanwhile, for the asparagus, trim off the lower third of the stems and discard. Halve the asparagus diagonally. For the broccoli, using a small knife, cut off the florets from the stem (halve the florets, if necessary, so they are all in bite-size pieces).
Line a baking sheet with paper towels and have ready. Set a colander in a bowl of ice water and have ready. Once the water is boiling, blanch each green vegetable separately, transferring each with a slotted or wire mesh spoon to the colander in the ice water bath after blanching, and letting the water in the pot return to a boil between each one. Blanch in this order: the peas, boiling for 1 minute; then the broccoli, boiling for 1-1/2 minutes; then the asparagus, cooking until al dente, 1 to 2 minutes, depending on the thickness of the stalks. Remove the blanched vegetables from the ice water and let them dry on the prepared baking sheet.
Separate the leaves of Bibb lettuce, discarding the large, tough outer leaves. Wash and dry completely. Shave the radishes into paper-thin slices with a mandoline.
To assemble the salad, dress all of the vegetables and lettuce lightly with the vinaigrette and place in a bowl. Using a vegetable peeler or mandoline, shave the Parmesan over the salad to garnish.