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Sprinkle the work surface with a little flour. Cut a quarter of the dough and roll the dough flat. Cut the dough into strips 1/2-inch wide and then each strip about 2 to 3-inches long. Using your thumb and index finger, gently pinch the width of the dough strip, and then roll out. Repeat the above process until all the dough is used up. Cover up any excess dough with a cloth to prevent it from drying, if you are not using it immediately.
Put the dough-strips on a lightly floured board and then add to a pot of boiling salted water. Stir to prevent the pasta from sticking together and drain when the pasta floats to the surface, 2 to 3 minutes. Reserve 1/4 cup pasta water.
To make the sauce: Add the olive oil, chopped rosemary, and Parmigiano cheese to a cold saucepan. Add the cooked strozzapreti to the saucepan with a 1/4 cup pasta water and mix well.