How to Make It
Preheat the oven to 375°. Stand the beets in a baking dish and rub them with the olive oil. Cover with foil. Bake for about 1 hour, or until the beets are tender when pierced.
Meanwhile, in a medium bowl, toss the shallots with the rice vinegar and red wine vinegar. Add 1/4 teaspoon salt and season with pepper.
Peel the beets and cut them into chunks. In a food processor, pulse the beets until finely chopped; do not puree. Add the beets to the shallots and toss. Refrigerate until chilled.
Cut off the top 3 inches of the endives and reserve. Halve and core the rest of the endives, then thinly slice crosswise. Toss the sliced endives with the walnut oil and season with salt and pepper. Mound the sliced endives on plates and arrange the spears around them. Toss the beets and spoon them onto the endive spears. Garnish with the cheese and serve.