Bring a covered pot of lightly salted water to a boil over high heat. Meanwhile, wash the beets well to remove the sand. When the water reaches a boil, add the beets. Cover the pot and cook the beets at a high boil for about 20-40 minutes, depending on size, until they are just fork-tender.
Using a slotted spoon, transfer the cooked beets to a colander. Any remaining sand from the beets will be left behind in the water, so just drain it into the sink. Set the beets aside until they are cool enough to handle, then remove the skin using your fingertips. The skin should slip off easily, and you can use a paring knife to remove any skin that remains. Cut the beets into medium-thick slices and arrange them in a row on a platter.
Using a sharp paring knife, remove the skin and the white pith from the oranges; do this over a bowl so that you can collect any juices. Cut the oranges into thin rounds. Arrange the orange rounds in between the slices of beets. Scatter the onion ribs evenly over the beets and oranges. Scatter the cheese and the chopped nuts evenly over the top. Drizzle the salad first with olive oil and then with vinegar. Sprinkle lightly and evenly with sea salt and pepper. Serve immediately.