I have experimented with making homemade coloured pasta, namely red (tomato) and green (spinach) and the result was rewarding, and incidentally rather delicious.
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.