Preheat oven to 425°.
Trim beets, reserving greens. Wrap beets in foil. Place beets and shallots on a baking sheet coated with cooking spray. Coat shallots with cooking spray. Bake at 425° for 25 minutes or until shallots are lightly browned. Remove shallots from pan. Return beets to oven; bake an additional 35 minutes or until beets are tender. Cool. Peel beets; cut into 1/2-inch wedges. Place beets, shallots, vinegar, rind, 1 teaspoon oil, and 1/4 teaspoon salt in a large bowl; toss well.
Heat remaining 1 teaspoon oil in a large nonstick skillet over medium-high heat. Add reserved beet greens to pan; sauté 1 minute or until greens begin to wilt. Stir in sugar, cider, and remaining 1/4 teaspoon salt; cook 30 seconds, stirring constantly. Remove pan from heat. Add arugula; stir just until wilted. Place about 1 cup greens mixture on each of 4 plates. Sprinkle each serving with 1 1/2 teaspoons walnuts; top each serving with 3/4 cup beet mixture.