Heat a generous drizzle of extra virgin olive oil in a large, deep skillet or Dutch oven over medium heat. Add the onion and cook until soft and translucent, about 5–7 minutes.
Add the zucchini, sliced garlic, and basil. Season generously with salt and cook for 5–6 minutes, stirring occasionally, until the zucchini begins to soften.
Pour in the 5 cups of water and bring to a simmer. Cook for 5 minutes.
Using a ladle, transfer about half of the zucchini mixture to a blender and blend until completely smooth.
Add the tubetti or ditalini to the pot along with the blended zucchini purée. Stir well to combine.
Cook, stirring frequently, until the pasta is al dente and the sauce is creamy, adding a splash of water if needed to maintain a silky consistency.
Turn off the heat and stir in the Parmigiano Reggiano until melted and creamy.
Divide among serving bowls and top each with a generous spoonful of stracciatella. Finish with a drizzle of extra virgin olive oil and serve immediately.