Preheat oven to 400°F. Wrap each beet individually in aluminum foil, and place on a baking sheet. Bake beets in the oven for 45 minutes, or until easily pierced with a fork.
Once done, remove from oven, and allow to cool until you can handle them. Cut off the ends of the beets, peel, and cut into 1/2 inch cubes.
In a small bowl, whisk together shallots, parsley, olive oil, and balsamic vinegar.
Season to taste with salt and pepper.
Before serving, toss beets with prepared vinaigrette, and top with feta cheese and hazelnuts. Serve cold or at room temperature.