1. Heat oil in large saucepan over medium heat. Add leeks and garlic, and sauté 5 minutes, or until leeks are softened and translucent. Add broth, artichokes, potatoes, thyme, and 2 cups water; cover, and bring to a boil. Reduce heat to medium-low; season with salt and pepper, if desired; and simmer, partially covered, 20 to 25 minutes, or until potatoes and garlic are very tender.
2. Remove thyme sprigs, and strip remaining thyme leaves into soup pot. Transfer soup to blender or food processor, and blend until smooth. Return to pot and stir in lemon juice. Season with salt and pepper, if desired. Ladle soup into bowls, and garnish each serving with 1 Tbs. prepared pesto.