This salad has changed the minds of many who previously found beets overpowering. The Sherry vinegar provides a nice accent, though balsamic vinegar also will work. The walnuts may be replaced with pine nuts, pecans, or slivered almonds.
In a baking pan toast walnuts in one layer in middle of oven until golden and fragrant, about 10 minutes. Cool nuts and coarsely chop.
Trim beet stems to about 1/2 inch. In a large saucepan simmer beets in water to cover until just tender, about 30 minutes. Drain beets. When beets are just cool enough to handle, peel and slice crosswise into 1/8- to 1/4-inch-thick slices. While beets are still warm, in a bowl toss with vinegar. Beets and nuts may be prepared 2 days ahead and chilled separately, covered.
Toss beets with nuts, oil, parsley, and pepper and season with salt.