Preheat the oven to 400°F. Cut the stems and tails off the beets and trim both ends off the onions. Do not peel. In a baking dish, toss the beets and onions with the olive oil and season with salt and pepper. Roast until tender, about 30 minutes for small beets, or about 1-1/2 hours for large beets, and 30 minutes for the onions.

Arrange the hazelnuts in a small baking dish and place in the oven with the vegetables. Cook, shaking the pan occasionally, until the nuts are lightly browned and fragrant, about 20 minutes. Fold the nuts into a tea towel and let sit about 5 minutes, then rub them vigorously with the towel to loosen and remove the skins. Chop the nuts coarsely and reserve.

As the vegetables are done, remove them to a plate, let cool, then peel. Depending on their size, cut the beets in half or into thin slices. Cut the onions in half lengthwise.

In a medium bowl, combine the hazelnut oil, coriander, and orange juice. Whisk until well combined and season with salt and pepper.

Peel and remove the membranes from the oranges with a sharp paring knife. Cut the oranges in half lengthwise, and then crosswise into thin slices. Seed the slices and add to the bowl containing the dressing. Add the onions and toss well. Divide the orange slices and onions among 4 plates. Scatter the beets around the oranges and onions and drizzle the salads with any juices left in the mixing bowl. Sprinkle some of the grated cheese over each salad, if desired, and sprinkle with the reserved nuts. Serve immediately.