Adjust oven rack to middle position, and heat oven to 450°.
Heat oil or butter in a heavy-bottom Dutch oven over medium-high heat. Add onion and prosciutto or ham and squash; saute until tender, 4 to 5 minutes.
Stir in rice (can be removed from heat and covered for up to 2 hours in advance), then add wine, and simmer until the liquid has almost evaporated. Turn off heat. Add broth and water. Cover the pot with a sheet of heavy-duty foil, pressing the foil down so it’s concave and rests on the broth. Place a lid over the pot to ensure an even tighter seal.
Set pot in oven; cook for 25 minutes. Remove from oven. Use a potholder to remove lid and foil. Remembering that the handles are hot, set pot on low heat. Add shrimp now.
Stir mixture, adding water if necessary, until rice is cooked and a little chewy at the center, the liquid is creamy, and the flavors of the new ingredients have melded in, about 5 minutes. Stir in 1 cup of Parmesan cheese, peas, and/or parsley. Adjust seasonings, including salt and pepper, to taste.
Spoon into shallow soup plates, sprinkling each serving with shaved Parmesan.