As soon as you complete Giovanni's Ready to Rumble questline, he will provide you with another feat of bravery to complete. Sort of. I mean, according to the mythology, a basilisk can turn you to stone just by staring at you. So be quick when collecting those Basilisk Scales!
Ironically, Magnus gives you a quest by the same name at around the same time. Happily, though, there are elements in common, so you'll likely want to try to complete them concurrently.