Place the mushrooms in a medium mixing bowl and toss gently with the salt. Place a plate on top of the mushroom and weigh it down with a heavy object. Let the mushrooms sit for an hour. Drain, spread them on a clean towel and pat them dry.
Bring the vinegar to a boil in a medium saucepan over medium-high heat. Add the mushrooms, return to a boil, and boil until they have softened slightly but still have a nice meaty texture, 3-5 minutes. Drain and spread the mushrooms out on a clean towel and pat them dry. Let them dry until they are no longer damp, about 2 hours.
Combine the oil, mustard seeds, tarragon and lemon zest in a small saucepan over medium heat. Heat, stirring from time to time, to just below a simmer (look for small bubbles to appear). Remove from the heat and let cool slightly.
Place the mushrooms in a wide mouth pint-sized canning jar. Pour the infused oil over the mushrooms, adding more oil to submerge completely if necessary. Cover and refrigerate. To serve, bring to room temperature and remove only what you plan to use. Top the jar with oil as necessary to keep the remaining mushrooms submerged. Eat within 3 months.
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.
Add cumin, coriander and caraway seeds to a small stainless steel or cast iron skillet and toast over medium-high heat until lightly brown and fragrant, about 2 minutes. Remove from heat and add to a blender.
Heat 1 tablespoon olive oil in a 12" non-stick skillet over medium heat until shimmering. Add the mustard greens, stirring constantly, until wilted, about 1 minute. Remove from heat and add to the blender.
Add remaining ingredients to the blender and process until fully broken down, about 1 minute, scraping down the sides as necessary. Transfer to a clean storage container and refrigerate for a week or freeze for up to 6 months.
If you purchase larger, less tender mustard greens, you may need to extend the cooking time (the greens I purchased were the size of spring mix greens).
Heat the olive oil in a 12" skillet over medium heat until shimmering. Add the shallot and cook, stirring frequently, until softened, about 2-3 minutes. Add half of the cherry tomatoes, and cook, stirring frequently, until they have softened and have just started to break open, another few minutes. Remove from heat and carefully transfer to a blender. Add the remaining ingredients, including the other half of the cherry tomatoes and starting with just 1 teaspoon of white wine vinegar. Blend on high until a smooth sauce forms, about 1 minute. Taste and add another teaspoon of white wine vinegar if the sauce needs a little extra zing. Transfer sauce to a freezer safe container, leaving at least 1" headspace if planning to freeze, and cool to room temperature. Store in the refrigerator for 1 week or the freezer for up to 1 year.