1. Heat 3 TBSP olive oil in medium pot over medium heat. Add onion and garlic, stirring occasionally until soft and glistening (6 minutes). Add paprika, half the coriander, and salt; cook until oil turns deep red (about 1 minute). Add carrots, parsnips, and just enough water to cover (about 3 cups).
2. Bring to a simmer and cook until carrots are tender (20 minutes). Remove veggies with slotted spoon; keep cooking liquid until thick and slightly reduced (about 10 minutes more). Season with pepper to taste; return veggies to broth.
3. Heat remaining TBSP oil in small skillet over medium heat. Add rest of coriander and toast for a minute. Stir parsley into yogurt; season with salt and pepper. Transfer to serving bowl; drizzle on flavored coriander oil. Spoon vegetables onto platter with some cooking liquid. Serve with yogurt-coriander sauce.