Preheat the oven to 400°. Line a half sheet pan with parchment.
Toss the carrots and beets with the caraway seeds, oil, and a generous sprinkle of salt and pepper. Toss until evenly coated, then spread in a single layer on the prepared pan. Roast until tender and golden, 45 to 50 minutes.
Meanwhile, zest the lemon directly into the yogurt in a medium bowl. Stir in the dill leaves and a generous sprinkle of salt and pepper.
Cut the lemon into quarters and squeeze 1 wedge all over the vegetables when they come out of the oven. Reserve the other quarters for another use.
Divide half the yogurt sauce among serving cups or dishes. Top with the vegetables, remaining yogurt, walnuts, and dill sprigs.
Recipe by Genevieve Ko.