In a large pot, bring 4 quarts water to a boil, but don’t salt it. Line a plate with a paper towel.

In a 12-inch high-sided sauté pan or skillet, heat olive oil over medium high until it reaches 350°F. If you don’t have a thermometer, test to see if the oil is hot enough by carefully placing a slice of zucchini into the oil. If it immediately starts to sizzle, it is ready.

Carefully add the zucchini slices to the pan in a single layer. You will need to cook them in batches, so as not to overcrowd the pan. Cook until the zucchini is golden on one side, about 5 minutes, then flip and cook an additional 3 to 4 minutes until both sides are evenly browned. If the zucchini starts to brown too quickly, lower the heat to medium. Use a slotted spoon to transfer the zucchini to the paper towel-lined plate. Repeat the process until all of the zucchini has been cooked. Turn off the heat and set the pan aside while you cook the spaghetti. Sprinkle ½ teaspoon fine sea salt over the cooked zucchini and toss to evenly distribute the salt.

Once the water is boiling, add the spaghetti and cook until al dente, about 8 minutes or according to the package instructions. Reserve 2 cups of the pasta cooking water, then drain the spaghetti through a colander.

Return the zucchini to the pan you fried it in, and add the spaghetti. Warm over medium heat for 2 minutes, gently stirring. Drizzle in 1 cup of the pasta cooking water. Use tongs to toss and stir to evenly coat the noodles. The sauce will start to thicken slightly at this point from the first addition of the pasta water. Turn off the heat.

Keep stirring and gradually sprinkle in half of the grated cheese. Roughly tear in half of the basil leaves and add to the pan with the remaining ½ teaspoon fine sea salt, black pepper, and remaining 1 cup of pasta cooking water. Use the tongs to stir the mixture to combine the ingredients into a shiny, silky sauce. Add the remaining cheese and vigorously stir until the sauce comes together, is creamy, and coats the spaghetti.

Roughly tear the remaining ½ cup basil leaves, add to the pan, and stir to mix in. Garnish with more cheese and basil if desired and serve immediately.