Cook the spaghetti in salted boiling water until al dente, according to package instructions.
While the pasta cooks, slice the zucchinis into thin rounds or half moons.
In a large pan, heat the olive oil over medium heat. Add the crushed garlic and sauté for about 1 minute until fragrant.
Add the sliced zucchinis to the pan and sauté until they become tender and lightly browned, about 8-10 minutes.
Remove the garlic clove and discard it. Reserve some pasta cooking water, then drain the spaghetti.
Add the drained spaghetti to the pan with the sautéed zucchini, tossing to combine.
Gradually add the grated Parmigiano-Reggiano cheese, tossing briskly to incorporate. Add reserved pasta water as needed to achieve a creamy consistency.
Season with salt and additional cheese to taste, and serve immediately, garnished with fresh basil leaves.