1Remove greens from beets, leaving about 1/2 inch of stem. Do not trim or cut root. Wash beets well. Place beets in 2-quart saucepan; add enough water to cover. Cover and heat to boiling; reduce heat. Simmer 40 to 50 minutes or until tender; drain.
2Cool beets 1 hour. Remove skins from beets under running water; drain beets on paper towels. Cut beets into julienne strips; place in shallow glass or plastic dish.
3In tightly covered container, shake oil, vinegar, mustard and sugar. Pour over beets. Cover and refrigerate at least 2 hours but no longer than 12 hours. Let stand at room temperature 30 minutes before preparing salad.
4Arrange beets on 4 salad plates. Top with arugula and cheese. Drizzle with remaining oil mixture if desired. Sprinkle with walnuts. Serve immediately.