Prepare the Zucchini: Wash the zucchini thoroughly and slice them into thin rounds. Heat a generous amount of extra virgin olive oil in a large pan over medium heat.
Cook the Zucchini: Once the oil is hot, add the zucchini slices in batches. Fry them until they are golden brown, about 3-4 minutes per side. As each batch is cooked, remove the zucchini and place them on a plate lined with paper towels to absorb excess oil. Sprinkle the zucchini with a pinch of salt while they are still warm.
Cook the Pasta: In a large pot of boiling salted water, cook the spaghetti until it is al dente, about 8-10 minutes, according to package instructions.
Prepare the Sauce: In the same pan used to fry the zucchini, add the garlic cloves and sauté until they are golden, then remove them from the pan. Add the fried zucchini back into the pan and lower the heat. Add a ladle of pasta cooking water to the zucchini and stir to create a light sauce.
Combine Pasta and Sauce: Drain the spaghetti, reserving some of the pasta water. Add the spaghetti to the pan with the zucchini. Stir well to coat the pasta with the zucchini sauce. Gradually add the grated Provolone del Monaco cheese, stirring constantly. If the sauce becomes too thick, add more pasta water a little at a time until the sauce is creamy and smooth.
Final Touches: Tear a few fresh basil leaves and add them to the pasta. Stir well and season with salt and pepper to taste.
Serve: Serve the pasta immediately, garnishing with extra grated Provolone and a drizzle of olive oil if desired.