Preheat oven to 425 degrees F. In a shallow baking pan combine carrots, parsnips, and onion. Drizzle with oil; toss to coat. Spread vegetables in a single layer. Roast, uncovered, 35 to 45 minutes or until tender.
In a blender or food processor combine roasted vegetables, broth, 1 cup water, and the paprika. Cover and blend or process until smooth.
Transfer soup to a large saucepan. Add additional 1/2 cup water, if needed, to reach desired consistency. Bring just to boiling; remove from heat. Season to taste with pepper. If desired, in bowl stir together yogurt and milk. Swirl yogurt mixture into soup. Top with chives and, if desired, serve with lemon wedges.