Preheat the oven to 400 degrees F with the rack in the middle. Trim and halve the beets lengthwise, and place in a 13-by-9-inch roasting pan. Fill with enough water so it comes halfway up the sides, cover the top tightly with foil and roast the beets for 30 to 40 minutes (depending on beets' size), until fork-tender. Remove from the oven, let cool, and slip the skins off. Using the coarsest setting on the food processor or the hand grater, shred the beets.
In a large bowl, toss the beets with the remaining ingredients and mix until well-combined. Taste and adjust seasonings accordingly, if needed. Serve immediately or refrigerate.