Heat a drizzle of olive oil in a large pot over medium heat. Add onion, prosciutto ends, and basil. Sauté until soft and translucent.
Add diced potatoes and cook for 2–3 minutes. Pour in passata and add 48 oz water. Season with salt and pepper.
Bring to a boil, reduce to a gentle simmer, and cook 30–40 minutes until potatoes are tender.
Add pasta directly into the pot. Stir occasionally and cook until al dente. The starch will naturally thicken the sauce. Add more water if needed for consistency.
Turn off heat. Stir in Parmigiano. Serve hot with extra cheese and a drizzle of olive oil.