1 pound beets, ends trimmed
2 Tbs. olive oil
2 Tbs. red wine vinegar
1 oz. Parmesan cheese, shaved with a vegetable peeler (optional)
salt and freshly ground pepper, to taste
Preheat oven to 400°F. Line a roasting or baking pan with aluminum foil and add beets in a single layer. Cover with another sheet of foil and roast for 1 hour. After 1 hour, check for doneness with a fork: if the fork pierces the beets easily, they are done. If not, roast for another 15 minutes and check again. Continue checking every 15 minutes until done. Do not overcook; this will make them more difficult to slice thinly. Remove from oven and let stand until cool enough to handle. Using fingers, rub off the skins, then slice as thinly as possible using a mandoline or a sharp knife.
In a small bowl, whisk together the olive oil and vinegar. Arrange beet slices on a large platter or several small salad plates so that slices are minimally overlapping. Drizzle with oil and vinegar mixture, then sprinkle with salt and freshly ground pepper. Sprinkle with shaved Parmesan, if using. Arrange a handful of mixed greens on top of each plate.