Prerequisites: Max out Olive's level 1 friendship
Reward: None
Unlocks: Olive friendship level 2, Moonbury's Heritage
(I fully admit that I was distracted in the three seconds where the name of this quest flashed up. 'Olive's Story 1' will do until I figure out the real name. My bad.)
The owner of the Willow Waters Bathhouse in the northeast of Moonbury Town, Olive predictably spends much of her time during the day tending to the main desk of the Bathhouse. If you're trying to hunt Olive down to improve your relationship with her then the Bathhouse is the first place you should look. She occasionally wanders the rest of the town, as well and, it's not unusual to see her at the beach, the Tailor's, or the Tavern. (In short, if you don't find Olive at the Bathhouse, use your dog to track her down.)
Once you've maxed out the first level of your relationship with Olive you'll see a notice from Ottmar on the Bulletin Boards of Moonbury, inviting everyone to try out a new recipe at his Beach Cafe. You'll need to visit the Cafe from Monday to Sunday, 16:00 to 22:00. The Cafe is on the beach in the northwest of Moonbury, in front of the Primerose Sail.
(It's possible you need to go on days where the Cafe is actually open, rather than any day of the week. I couldn't get the quest to spark until I did that. The Cafe is open Wednesday, Thursday, and Saturday.)
Head up onto the beach at the correct time and you'll see a lineup for Ottmar's grilled corn. Olive is critical of Ottmar's claims that it's the 'best on the continent', and soon makes it very obvious that she kind of hates Moonbury Town. The quest ends once she stops complaining and leaves, unlocking the second level of your relationship with her. Continue to befriend Olive to unlock the next quest in her story, Moonbury's Heritage.