Cook bacon in large pot over medium heat until crisp. Using slotted spoon, transfer bacon to paper towels. Add oil to drippings in same pot; heat over medium heat. Add leeks; sauté until tender but not brown, about 7 minutes. Add parsnips, carrots, garlic, and thyme; sauté 5 minutes. Stir in potatoes, then flour; stir 1 minute to coat. Gradually add milk and 3 cups broth; bring to boil. Reduce heat; simmer uncovered until vegetables are tender and soup thickens slightly, stirring occasionally, about 20 minutes. Season with salt and pepper. (Can be made 1 day ahead. Cover and chill bacon. Cool chowder slightly. Chill uncovered until cold, then cover and keep chilled. Rewarm before continuing, thinning with more broth, if desired.)
Stir bacon into chowder. Ladle into bowls. Sprinkle with parsley; serve.