If your Parmesan is genuine Parmigiano Reggiano, I have to tell you that it can't be vegetarian. The law states that it must be made with calf rennet. That's fine for you and me, but if I'm cooking a pasta bake or anything else that is meat-free for vegetarians I ask them in advance without pressure whether Parmesan is acceptable. You may need to check out your mozzarella on this score too. Several other cheeses are, as far as I know, always made with animal rennet, including pecorino romano, emmenthal, Gorgonzola, manchego and gruyere. Of course, what the eye don't see... But I can't work that way!