Bring water to a rolling boil. Add the squash, potato and the salt. Cook for 2 minutes, add the pasta, and cook until it offers considerable resistance to the tooth, about three quarters the recommended cooking time.
While the pasta is cooking, put the garlic, hot pepper, and parsley in a large non-stick skillet and drizzle with 1 tablespoon extra virgin olive oil. Place the skillet over moderate heat and when the garlic begins to sizzle remove from heat.
Drain the pasta and the vegetables, reserving 2 cups of the cooking water.
Put the drained pasta and vegetables in the skillet with the garlic and add 1 cup pasta cooking water. Cook over highest heat, stirring until the pasta is cooked, surrounded by a creamy sauce. Add more cooking water if the sauce dries out.
Serve the pasta on bowls, topped with a drizzle of olive oil and cheese.