Bring a large pot of lightly salted water to a boil. Add the pasta and cook until just tender, about 8 to 10 minutes.
While the pasta cooks, set a very large skillet over medium heat and add the oil. Add the mushrooms and cook until tender, about 5 minutes. Add the snap peas, pesto and stock and bring to simmer. When the pasta is cooked, reserve 1/2 cup of its cooking liquid, and then drain the pasta well. Add the pasta and reserved cooking liquid to the skillet, season with salt and pepper, and toss to combine. Serve, tableside, with Parmesan cheese.
Note: To blanch snap peas, cook in boiling water 1 minute. Cool in ice-cold water, and then drain well.