Bring a large, salted pot of water to a boil. Cook the pasta till al dente, according to package instructions or for a minute less.
As the water heats and pasta cooks, heat the butter or oil in a large, deep, nonstick skillet over medium heat. Add the mushrooms and garlic. Cook, stirring often, until the mushrooms have released all of their juices and reduced considerably in size, about 7-8 minutes.
Add the white wine to the skillet. Continue cooking the mushrooms and garlic, stirring often, until the wine has almost completely cooked down.
Add the broth to the skillet and continue to cook the mushrooms, stirring often, for 2 more minutes. Stir the cashew cream and salt into the mushrooms. Reduce the heat to low.
As soon as the pasta is ready, drain it, reserving a cup of cooking water. Add the drained pasta to the skillet with the creamy mushroom sauce. Stir everything together and continue to cook over low heat. Add the thyme, freshly ground black pepper to taste, and the cashew parmesan cheese (or vegan parmesan of choice). The pasta should be creamy and have some looseness; if it starts to thicken, stir in a half cup (or so) of pasta cooking water to loosen it up. Serve the pasta right away, with extra cashew parmesan or fresh herbs if desired.
*To omit the white wine, simply skip step 3 of the instructions.