Heat sunflower oil in a deep fryer or heavy pot to 350°F (175°C).
Working in batches, fry zucchini slices until golden brown and slightly crisp, about 2-3 minutes. Transfer to paper towels to drain excess oil.
Place fried zucchini in a bowl and lightly season with salt. Allow to rest for at least 6 hours or overnight. This resting period is crucial for developing flavor.
When ready to prepare the pasta, bring a large pot of salted water to a boil. Cook spaghetti until al dente, reserving 1 cup of pasta water before draining.
While pasta cooks, melt butter in a large skillet over medium heat. Add minced garlic and sauté for 30 seconds until fragrant.
Add fried zucchini to the skillet and gently stir. Break up about half the zucchini slices while leaving others whole.
Add 1/2 cup of reserved pasta water and bring to a simmer.
Add drained pasta to the skillet, along with both cheeses. Toss continuously to create a creamy sauce, adding more pasta water if needed.
Finish with torn basil leaves, freshly ground black pepper, and a final drizzle of olive oil.
Serve immediately, garnished with additional cheese and basil if desired.