Heat oil in a large deep skillet over medium-high heat. Add zucchini and onion and sprinkle with 1/2 teaspoon salt. Cook until onion softens, 2 to 3 minutes. Add basil and cook for 1 minute, stirring often, until vegetables begin to soften, about 5 minutes.
Add water and simmer until very tender, 7 to 9 minutes.
Remove about half the zucchini mixture and liquid from the skillet and transfer it to a blender or food processor. Remove the cap from the top to allow steam to escape and cover loosely with a towel. Blend until smooth. Return mixture to the pan.
Stir in pasta, remaining salt, and stock if using. Add water as necessary to just cover.
Bring mixture to a simmer, and cook, stirring occasionally until pasta is al dente and mixture is creamy, about 11 to 13 minutes. Add additional water or stock if liquid has evaporated too much before the pasta is cooked.
Stir in Parmesan cheese and pepper. Season to taste with salt. Serve topped with more basil, cheese, and pepper.
