Remove the central ribs from the kale and slice leaves thinly. Cook beets in boiling water until tender when pierced with a fork, about 20 minutes. Remove from pan and drain. When cool enough to handle, remove outer peel of beets with hands, a paper towel or a vegetable peeler. Cut into ½-inch dice. (Note: When working with beets, you may want to use food-safe plastic gloves to avoid staining hands.)

Whisk together vinegar, shallots, oil, lemon juice, salt and pepper until emulsified. Place sliced kale in a large salad bowl and toss with half the dressing. Allow to rest for 20 to 30 minutes. Divide among 4 plates and arrange beets, apple slices and chestnuts on top; add cheese, if desired. Drizzle with remaining dressing and serve.