Can you eat parmesan when you are breast feeding?

Yes
It's safe to eat whilst you're breast feeding, though it can affect you it is unlikely to affect your baby.
Parmigiano-Reggiano (IPA: [ˌparmiˈdʒaːno redˈdʒaːno]), also known in English as Parmesan (pron.: /ˌpɑrmɨˈzæn/ or pron.: /ˌpɑrmɨˈʒæn/), is a hard, granular cheese, cooked but not pressed, named after the producing areas near Parma, Reggio Emilia, Modena, and Bologna (all in Emilia-Romagna), and Mantova (in Lombardia), Italy. Under Italian law, only cheese produced in these provinces may be labelled "Parmigiano-Reggiano", while European law classifies the name as a protected designation of origin.
Granular cheese, also known as stirred curd cheese and hard cheese, is a type of cheese produced by repeatedly stirring and draining a mixture of curd and whey. It can refer to a wide variety of cheeses, including the grana cheeses such as Parmigiano-Reggiano (at right) and various others. Many types are commonly used in the production of processed cheese, especially American cheese, which by law must consist of Cheddar cheese, Colby cheese, cheese curd, or granular cheese.