Prerequisites: Max out Osman's level 1 friendship
Reward: None
Unlocks: Unlock Osman level 2 friendship, Taking a Break
Osman is one of the trickier residents of Moonbury to track down and befriend, though you will likely see him often. Osman patrols the streets of Moonbury quite a bit, and can be found all over the place. The only stable places you might find him are the Police Station, usually around midday, and at home, either in the morning or at night. Osman gets out of bed around 8:00 so catching him before he leaves the house is your best bet for building a friendship.
Once you've maxed out the meter for your first level of friendship with Osman a notice will appear on the town's Bulletin Boards, inviting residents to try out Yorn's new recipe at the Lazy Bowl Tavern. Go to the Tavern between 18:00 and 23:00, Tuesday to Sunday, and you'll watch a quick scene with Osman. Sounds like the guy doesn't get many breaks.
Completing the scene will end the quest, and you'll be moved to the second tier of friendship with Osman. (And, no, you don't actually need to pay his tab.) This will allow you to proceed to the next quest in Osman's storyline, Taking a Break.