Using a mandoline or a sharp knife, very thinly slice the beets, carrots, celeriac, and fennel; place in a medium bowl. Set aside.
Drizzle with oil and lemon. Season with chile, salt, and pepper. Sprinkle with parsley; toss to combine. Transfer to a serving platter.
Hold the pomegranate above the salad, cut-side facing down. Using a rubber spatula in the other hand; strike the pomegranate releasing the seeds and juice onto the salad. Serve immediately.