Prep the mushrooms. Wipe off any dirt patches with a paper towel or clean kitchen towel. Depending on the variety, slice them or tear them with your hands (oyster and maitake are much easier to tear than slice).
Prep the leeks. Slice off the dark green tops and discard or save for making vegetable broth. Cut each leek in half vertically and then slice horizontally, but not too thinly, as they’ll cook down with the mushrooms for quite a while.NOTE: Leeks are very dirty, so you need to wash them at this stage. Submerge chopped leeks in a bowl of cold water, run your hands through the bowl to loosen the dirt, and then scoop the leeks out using your hands or a slotted spoon. Pat dry the washed leeks.
Heat a large sauté pan with deep sides (or a Dutch oven) over medium-high heat and add 1 1/2 to 2 tablespoons of olive oil. Once the oil is shimmering, add HALF of the leeks and mushrooms. Cook for 8 to 10 minutes until mushrooms are nicely browned, stirring occasionally but not too frequently.
Reduce the heat to medium and add HALF of the garlic, HALF of the thyme, and 1/4 teaspoon kosher salt. Cook for 2-4 minutes, or until the mushrooms are browned and crispy. When done cooking, transfer this batch to a plate or bowl. Repeat the process with the remaining oil, mushrooms, leeks, garlic, thyme, and salt.
While the mushrooms are cooking, make the “vegetable broth roux.” In a medium bowl, whisk together the vegetable broth, tamari, Worcestershire sauce (if using), and flour in. Whisk until until no clumps remain.
Pour the white wine into the pan with the cooked mushrooms, and use a wooden spoon or flat-ended spatula to deglaze the pan by scraping up any brown bits on the bottom of the pan. Reduce the heat as needed to simmer for 3 minutes, or until the smell of alcohol has dissipated and the wine has mostly evaporated.
Pour the vegetable broth roux into the pan and whisk to combine, ensuring there are no clumps. Bring to a simmer, then pour in the coconut milk, tahini, nutritional yeast, ½ teaspoon kosher salt, and paprika. Bring to a simmer over medium-low heat. Cook for 10 minutes, until the sauce is thickened and very creamy.
Meanwhile, cook the pasta. Bring a large saucepan of salted water to a boil. Cook the pasta according to the package instructions until al dente. Drain and keep warm.
Stir the Dijon mustard into the stroganoff sauce and stir. Add the hot cooked pasta and chopped dill (or parsley), and toss to coat.
Divide the pasta among plates or bowls, and top each with a handful of the first batch of crispy mushrooms and extra dill (or parsley) to garnish.