Pecorino is traditional and is what I usually keep in the fridge, so is what I use here. Natoora's one is a cut above any other I've tried, even though it is a bit pricy. But, it honestly does not matter if you switch in parmesan or Grana Padano - just make sure if you're feeding this to a pescatarian that no animal products are in the cheeses, as Italian hard cheeses like this often contain them.