Melt the butter in a large saute pan; add in the chopped zucchini, onions, and salt; saute over medium ehat for 10-15 minutes, until the veggies are very soft without browning; set aside to cool for 20 minutes.
In batches, puree the zucchini-onion mixture with the parsley; return the sauce to a clean saute pan; place over low heat.
Bring a big pot of water to a boil; add salt and then add the rigatoni; cook to al dente.
Drain, reserving ½ cup of pasta water.
Toss the pasta in the sauce, adding some of the pasta water if the sauce is too thick.
Serve right away sprinkled with shredded zucchini and Parmigiano-Reggiano and a drizzle of olive oil.