1. Preheat oven to 425°.
2. Leave root and 1-inch stem on beets; scrub with a brush. Place beets in a baking dish; bake at 425° for 1 hour and 10 minutes or until tender. Cool; peel and cut into 1/4-inch-thick slices.
3. Combine vinegar, oil, salt, and pepper, stirring with a whisk. Arrange beet slices in a single layer on a platter. Drizzle beets with half of vinegar mixture.
4. Combine remaining vinegar mixture and arugula in a large bowl; toss gently to coat. Top beets with arugula mixture. Sprinkle with cheese.