Step 4 is important. The dryer the broccoli rice is, the better the flavour and texture of the broccoli cakes will be.
Parmesan cheese is not truly vegetarian, as it contains animal rennet. To make this dish 100% vegetarian, omit the cheese or find a suitable vegetarian substitute made without animal rennet. In supermarkets look for the 'parmesan style hard cheeses' which are suitable for vegetarians.