Bring a large pot of salted water to a boil and cook the pasta until al dente, about 8 minutes. Drain and set aside.
While the pasta cooks, heat olive oil in a large skillet over medium heat until shimmering. Add the sliced mushrooms and sauté for 8-10 minutes, stirring occasionally, until they turn deep golden brown and release their juices.
Push the mushrooms to one side of the skillet and add the diced onion to the cleared space. Sauté for 3-4 minutes until translucent and fragrant, then add the minced garlic. Cook for another 30 seconds until fragrant, stirring constantly to prevent burning.
Pour in the warmed vegetable broth, scraping up any browned bits from the bottom of the skillet. Bring the mixture to a gentle simmer and cook for 2-3 minutes, allowing the flavors to meld.
Reduce the heat to low and stir in the plant-based sour cream or cashew cream, mixing until smooth and creamy. Let it simmer gently for 4-5 minutes until slightly thickened, then season with salt, black pepper, and smoked paprika if using.
Add the cooked pasta directly into the skillet with the mushroom sauce. Toss gently to coat every strand with the creamy sauce, adding a splash of reserved pasta water if needed to loosen the sauce.
Taste the dish and adjust the seasoning, adding more salt, pepper, or a squeeze of lemon juice for brightness. Let it sit for a minute to allow flavors to meld.
Serve the vegan mushroom stroganoff hot, garnished with chopped herbs or a drizzle of olive oil if desired, and enjoy the rich, comforting flavors.