Combine first 6 ingredients in a large stockpot; bring to a boil. Partially cover, reduce heat, and simmer 30 minutes or until vegetables are tender. Place half of potato mixture in a blender; process until smooth. Repeat with remaining potato mixture. Return pureed potato mixture to pan; stir in wine and salt. Cook over medium heat for 3 minutes or until thoroughly heated. Remove soup from heat, and stir in milk.
Divide soup evenly among 6 bowls; drizzle oil evenly over soup. Sprinkle with onions.