Preheat oven to 400°F. Wrap beets and potatoes separately in foil; seal tightly. Roast on oven rack until tender when pierced with skewer, about 45 minutes for potatoes and 1 1/2 hours for beets. Unwrap and cool completely.
Peel beets; cut into 1-inch pieces and place in blender. Add milk, 2 tablespoons onion, 2 tablespoons chopped dill and vinegar; blend until smooth. Season to taste with salt and pepper. Refrigerate soup until cold, about 1 hour.
Peel potatoes and cut into 1/4-inch dice. Place in medium bowl. Add remaining 2 tablespoons each of onion and chopped dill. Fold in yogurt. (Can be prepared 1 day ahead. Cover beet soup and potato salad separately and refrigerate.) Ladle beet soup into 4 bowls. Top with potato salad; garnish with dill sprigs.
