Using your hands, peel tangerines, and separate fruit into segments; pop out seeds, and place segments in a medium bowl. Slice kumquats into very thin rounds, and remove seeds. Add to bowl.
Using a mandoline or sharp knife, slice celery thinly on the bias. Add to bowl with fruit. Toss in walnuts.
In a small bowl, whisk together lemon juice and oil; season with pepper. Drizzle over citrus mixture in bowl, and toss to combine. Divide among four salad plates. Shave cheese over each salad, and serve immediately.