Steam the large beets until tender-firm when pierced with a knife, about 35 minutes. Steam the little beets until tender-firm, about 20 minutes. Chill both. Using 5 or 6 neat strokes of the knife, peel and trim the red beets. Slip off the skins of the smaller beets with your hands. Leave the smallest ones whole. Quarter and halve the rest.

Peel, then thinly slice the onions into rounds, toss with the vinegar, and sprinkle with salt. Refrigerate for at least 20 minutes.

To compose the salad, slice the large beets on a mandolin or very thinly by hand, then overlap them on a large platter. Scatter the small beets on top, then add the onions. Drizzle some of the vinegar over all, salt lightly, and season with pepper. Finely mince the parsley and the sprinkle with the dill over the salad. Add the arugula. Drizzle olive oil over all and serve.