Cook the linguini in plenty of rapidly simmering water until al dente. Drain, reserving about a cup of the cooking water.
Meanwhile, heat the oil in a large skillet. Add the garlic and sauté over low heat for about 2 minutes, or until golden.
Add the asparagus, mushrooms, dried tomatoes, and wine. Raise the heat to medium and sauté, stirring frequently, until most of the wine has evaporated and the asparagus is tender-crisp, about 6 minutes.
Combine the pasta and asparagus mixture in a large serving bowl and toss together. If the mixture needs more moistness, add about ¼ cup of the reserved pasta cooking water at a time. You want this dish to be moist, but not watery!
Season to taste with salt and pepper. Then serve, passing around the vegan Parmesan for topping if desired.