Place the beets and 1 tablespoon of the salt in a large pot and add enough cold water to cover by 2 inches. Bring to a boil, reduce heat to a simmer, and cook until a paring knife can be inserted smoothly into a beet, about 25 minutes, depending on size. Drain and rinse under cold running water until cool enough to handle. Remove the skins. (They should slip off easily, another sign of doneness.) Place the beets in a bowl and refrigerate for at least 1 hour. Slice them in half lengthwise. Arrange the halves on 6 serving plates. Drizzle with the oil and vinegar, then sprinkle with the remaining salt and the pepper. Serve with a dollop of sour cream on the side and some snipped dill.
Tip: Look for beets in an array of colors at your local farmers' market. Candy cane (pictured) is a relatively common variety with red and white stripes.