Preheat the oven to 350°F. Wash and dry the beets. Cut off the beet greens 1-inch from top of beets. Place the beets in a 9x9-inch baking pan and toss with 2 tablespoons of the oil, 2 tablespoons of the vinegar, and sprinkle with kosher salt. Cover the pan tightly with foil. Roast until the beets are just tender, about 1 hour. Cool slightly. Using a towel, rub off the peel and stems from the beets. Cut each beet into 6 wedges. Set the beets aside in a bowl with any liquid from the roasting pan.
Meanwhile, cook the farro in large saucepan of boiling salted water for about 20 minutes, stirring occasionally, or until tender. Drain. Transfer the farro to a large bowl and toss with the dried cranberries.
In a small bowl, combine the remaining 4 tablespoons of vinegar and the shallots. Whisk in the remaining 4 tablespoons of oil and season with salt.
In a large bowl, toss the arugula and fennel with some of the vinaigrette to coat lightly. Season with salt.
Spoon the farro-cranberry mixture over a platter. Top with the arugula and fennel, then top with beets. Arrange the hazelnuts and cheese around. Drizzle with more vinaigrette and serve immediately.