The quest becomes available at 50% friendship or rivalry after completing the quest Family Matter.
If you have 50% friendship then you get A Story Being Told.
If you have 50% rivalry then you get A Rumor Making the Rounds.
Speak with Varric at The Hanged Man.
After you begin the dialogue Varric talks about a rumor going around and a dialogue wheel pops up allowing you to investigate the situation a bit more. It turns out Varric is spreading tales about Hawke, the latest being either that Hawke "single-handedly fought off a pirate invasion at midnight, on the sacred ground of the chantry" (friend) or that Hawke and "a band of pirates tried to burn the chantry down in the middle of the night" (rival).
If you did not help Isabela in her recruitment quest a different tale is being told. The tale being "Hawke and that old coot Solivitus have gone into business together ... making love potions".
While we know Varric is telling a story to Cassandra we see the beginnings of the Champion of Kirkwall unfold and Hawke learns that Varric is telling tales. He describes how he tells his tales and makes a hero.
The quest is short lived and only exists within the cutscene dialogue and does not lead directly to any other quests.