Cook pasta according to package instructions in salted boiling water until al dente. Reserve 1-1/2 cups cooking water and drain pasta. Set aside for a moment.
Heat a large skillet over medium-high heat. Add olive oil to pan and swirl to evenly coat. Add zucchini and shallot to pan, season with salt and pepper, and sauté 4-6 minutes until zucchini is tender. Add garlic and cook 1 additional minute until fragrant.
Pour 1/2 cup pasta cooking water in pan and use a wooden spoon to scrape up any browned bits. Cook an additional 1-2 minutes until most of water is evaporated.
Combine sautéed zucchini, heavy cream, basil, Parmesan, and an additional 1/2 cup pasta water in a blender and blend on high speed until smooth. Season sauce with salt and pepper to taste.
Pour sauce back into the same pan you used to sauté the zucchini and set over medium heat. Bring sauce to a low simmer and fold in pasta. Cook 2-3 minutes until sauce is coating pasta, thinning with remaining 1/2 cup pasta water if needed.
Season pasta with additional salt and pepper to taste if needed and serve warm with additional fresh basil and cheese on top. Enjoy!