Line a rimmed baking sheet with a triple layer of paper towels and set aside.

Pour neutral oil and 1 cup olive oil into a large Dutch oven or large heavy-bottomed pot, heat oil over medium heat to 350°F (175°C).

Carefully place ⅓ of the zucchini rounds into oil and fry until light golden brown, 6 to 8 minutes.

Transfer fried zucchini to prepared lined baking sheet and sprinkle with ½ teaspoon kosher salt.

Repeat frying the remaining 2 batches of zucchini.

Bring a large pot of water to a boil over high heat.

Add remaining 2 tablespoons salt, return to a boil, then add spaghetti and cook until not quite al dente.

Reserve 2 cups of cooking water, then drain pasta.

In a large high-sided skillet, heat remaining 3 tablespoons olive oil over medium heat.

Add garlic and cook until fragrant, about 1 minute.

Add half of the fried zucchini and mash into a paste.

Add par-cooked pasta, 1 ¼ cups reserved cooking water, and remaining 1 teaspoon salt, cooking until sauce is emulsified.

Remove skillet from heat, add grated cheese, and stir rapidly.

Adjust sauce with reserved pasta water to desired consistency.

Season to taste with salt and pepper, transfer to a serving bowl, and garnish with remaining fried zucchini and basil.