Preheat the oven to 400 degrees F.
Put a large piece of aluminum foil on a baking sheet and put the beets on it. Drizzle olive oil over them and wrap them tightly in the foil, making a packet. Roast until a knife inserted into the largest beet meets no resistance, about 1 hour to 1 hour and 15 minutes. Cool and remove the skins by rubbing the beets with a paper towel. (Gloves are a good idea to prevent staining your hands.)
Cut the peel away from the oranges with a sharp knife, exposing the flesh. Hold the peeled orange in your hand and carefully slice the segments away from the membrane, dropping them into a bowl. Do not discard membrane. Thinly slice the beets and arrange on serving plates. Scatter the orange segments and hazelnuts over the sliced beets, drizzle the plates with olive oil and squeeze a little juice from the orange membrane over each plate. Season with salt and pepper, to taste. Garnish with shaved thin slices of cheese and serve.