Heat oil in a large saucepan over medium heat until shimmering. Add onion and cook, stirring occasionally, until soft and starting to brown, about 5 minutes. Add garlic and cook until fragrant, about 30 seconds. Add parsnip, celery root, potato and 6 cups liquid and bring to a boil. Reduce heat to a simmer and cook uncovered until vegetables are soft, about 15 minutes. Remove from heat and allow to cool for a few minutes.
Puree soup either by transferring to a blender (do not fill blender more than 1/2 full and process in batches) or puree in the saucepan using an immersion blender. Adjust the thickness by adding an additional 1-2 cups of liquid and mix to combine. Add the cream, sugar, vinegar, salt and sugar and adjust seasoning as needed.
To serve, portion soup into individual bowls and drizzle with truffle oil, toasted bread crumbs and a few leaves of parsley. Serve.
Heat butter in a Dutch oven over medium heat until foaming has subsided. Add the onion bulb and zucchini, along with 1 teaspoon sea salt and pepper to taste, and cook, stirring occasionally, until softened and just lightly browned, about 10 minutes. Add the garlic and cook, stirring often, until fragrant, about 1 minute. Add the stock and bay leaf, cover, and bring to a simmer and cook for 10 minutes. Remove the cover and add the onion greens and peas and simmer for another 2-3 minutes, or until the onion greens are just soft. Remove from heat, add fresh herbs (start with 1 tablespoon) and puree using an immersion blender (easier but you won't get a really smooth texture) or transfer to a blender in a couple batches (more time consuming but you get a smoother texture). Taste and adjust seasoning as needed, adding the additional tablespoon of herbs if desired. Serve immediately or cool to room temperature before storing in an air-tight container in the refrigerator. Garnish ideas are listed above in the "Variation" section.
1) you can serve this hot, room temperature or chilled, making it a great soup for any time of year; 2) I used parsley as the fresh herb addition when I garnished it with creme fraiche and then cilantro when I garnished it with tempeh, but I think basil or tarragon would be great as well.