Talk with Count Borhis di Salvaress at the Trading Post in the north of Toussaint and search for clues in the area. This will expand the quest and give you a choice of whether to kill the monster or not.
Can’t believe I reached level 34 without discovering Basilisks until now… Watch my stupid mistake as I run up to the beast and cast Yrden in its face, instead of Igni… Doh!
Monster Contracts are side quests in The Witcher 3 that you can take on for extra money and experience. You usually get Monster Contracts from notice boards.