Here is a quick run down on how I managed timing all the parts of this recipe...
Steep the mushrooms first and during that 30 minute waiting period, measure and prepare the asparagus, prosciutto, garlic, and basil. Grate the cheese and set aside. Start the pasta water, saving some room for the mushroom 'tea'. When the mushrooms are close to being ready to chop, heat the skillet. Drain the mushrooms and roughly chop and set aside. Add the 'tea' to the pasta water. Add the oil to the skillet and when hot, add the prosciutto. As the prosciutto cooks, add the pasta to the now boiling water and set the timer. Add the asparagus, then the mushrooms and while that is cooking and just before the pasta is ready, prepare the basil sherry cream mixture in the blender. Remove the prosciutto, asparagus, and mushrooms to a clean bowl and heat the remaining olive oil. Reserve the portion of the pasta water needed and drain the pasta when done. Add the flour to the oil and cook the roux, then add the pasta water and basil sherry cream mixture. Reduce the heat and when simmering, add the asparagus mixture and pasta, tossing to coat. Plate and sprinkle remaining cheese on top as a garnish.