Brown the mushrooms. Heat ½ tablespoon olive oil in a large skillet over medium-high heat. Add half of the mushrooms in a single layer and cook for about 5 to 7 minutes, stirring only occasionally, until browned around the edges and the released moisture has evaporated. Transfer to a plate. Repeat with another ½ tablespoon olive oil and the remaining mushrooms.

Cook the aromatics. Add the remaining 1 tablespoon olive oil and the sliced leek to the skillet. Cook for 3 to 4 minutes, stirring occasionally, until softened but not browned. Add the garlic and thyme and cook for about 1 minute, just until fragrant.

Mix the sauce. Whisk the vegetable broth, oat milk, flour, tahini, tamari, nutritional yeast, white miso, vegan Worcestershire if using, paprika, and salt in a bowl until completely smooth.

Thicken the sauce. Pour the mixture into the skillet and bring it to a gentle simmer. Cook for about 4 to 6 minutes, stirring regularly, until smooth and thick enough to lightly coat the back of a spoon.

Finish the stroganoff. Reduce the heat to low. Return the browned mushrooms to the skillet and stir in the Dijon mustard and most of the fresh dill.

Add the pasta. Add the drained pasta and toss until evenly coated. If the sauce is too thick, add reserved pasta water 1 tablespoon at a time. If it seems too loose, cook over low heat for another minute.

Taste and add more salt if needed, along with freshly ground black pepper. Finish with the remaining fresh dill and serve warm.