The Italian cheese made from cow's milk that is often grated over pasta is Parmesan.
Parmesan is a hard, granular cheese traditionally associated with Italy’s Emilia-Romagna region. The authentic Italian cheese is called Parmigiano Reggiano, and it is produced from unpasteurized cow’s milk before being aged for at least 12 months.
Its firm texture and concentrated savory flavor make it especially suitable for grating over pasta, risotto, soups, and salads. The cheese is also used in cooking because it melts and seasons dishes without adding much moisture.
Parmesan and Parmigiano Reggiano are related terms but are not always legally identical. In the European Union, “Parmigiano Reggiano” is a protected designation of origin, while “Parmesan” may describe locally produced imitations in some countries. Asiago and Romano are also Italian cheeses, but the wording of this question conventionally points to Parmesan.