In a large skillet over medium-high heat, fry the zucchini in hot oil until golden brown, working in batches if necessary. Drain on a paper towel lined tray for at least 5 hours or up to 24 hours.
Bring a large pot of salted water to a boil. Add the pasta and cook until about 3 minutes under al dente.
Meanwhile, put the butter and zucchini in a stainless steel recipient, preferably with two-handles, and add the basil and a small ladleful of the pasta cooking water. Place on a warm surface to slowly melt the butter/ meld the ingredients as the pasta cooks, or you can set up a bane marie, if you wish, as instructed in the video.
Drop in the pasta and a ladleful of the pasta cooking water, and toss briefly to amalgamate the ingredients. Add a few grindings of pepper and begin to toss until the liquids in the pan begin to be absorbed, about 1 minute.
Sprinkle in half of the cheese and toss until the sauce begins to thicken.
Continue to toss, sprinkling in the remaining cheese, until the sauce is dense and creamy and the pasta is al dente, about 2 to 3 minutes more - making any adjustments, by sprinkling in more cheese or water, as necessary.
Plate the pasta, and serve immediately.
