Step 1In a medium heavy-bottom soup pot heated over medium-high heat, saute the leeks in the butter until tender, 3 to 5 minutes, stirring frequently, and being careful not to burn the butter. Stir in the thyme and bay leaves and continue to cook until aromatic, about 1 minute.
Step 2Stir in the potatoes, parsnips, celery root and broth and bring the mixture to a good simmer. Season with one-half teaspoon salt and a pinch of pepper, or to taste. Cook until the parsnips begin to become tender, 15 to 20 minutes. Reduce the heat to a gentle simmer and stir in the cream. Continue to cook until all of the vegetables are tender, an additional 5 to 10 minutes. Remove and discard the thyme sprigs and bay leaves.
Step 3Puree the soup until smooth using a blender or immersion blender. Strain the soup through a fine mesh strainer and season as desired with additional salt and pepper. Add the truffle oil, a few drops at a time, to taste.
Step 4Ladle the soup into bowls and serve immediately.