Heat the ¼ cup of olive oil in a large skillet over medium heat. Working in batches if necessary, add the sliced zucchini and sauté, flipping once, until the zucchini is golden brown, about 3 minutes per side.
Transfer the zucchini onto a paper towel-lined baking sheet and sprinkle lightly with salt. Set aside.
Meanwhile, bring a large pot of well-salted water to a boil. Add the pasta and cook until very al dente (aim to have the pasta reach this point when needed to transfer to the skillet, as instructed below). Do not discard the pasta-cooking water.
In a separate large skillet (or clean out the first skillet), heat the remaining olive oil over medium low heat. Add the whole garlic cloves and allow to infuse the oil until cloves are golden and fragrant. Remove garlic and discard.
Add a ladle of the pasta-cooking water to the skillet along with at least half of the fried zucchini. Allow the mixture to come to a simmer, then use a wooden spoon to mash the zucchini.
Reserving the pasta-cooking water, use tongs to transfer the al dente pasta to the skillet with the zucchini sauce; continue cooking the pasta in this sauce for about 2 minutes.
Turn off the heat and allow the mixture to rest for about 1 minute. Add the cheese and toss with the tongs or by gently flipping the ingredients in the skillet until the mixture is emulsified. Add reserved pasta-cooking water, about 2 tablespoons at a time, until the consistency is creamy. See chef’s note.
Taste; season with salt or pepper to your liking. If using, add in the parsley and toss. Divide pasta among individual bowls, garnish with remaining fried zucchini and sprinkle with more pecorino, if desired.
Chef’s note: To avoid the cheese clumping when added, make sure to have the pan off the heat and toss well. If it does clump, adding some cooled down pasta water will help to loosen the cheese.