Cotton Sugarloaf Hat

Head, item level 22. Equip level 22, all classes.

From 125 Never Forget and 1 more quest.

From quests

125 Never ForgetChoose one of 4
127 Buried TruthChoose one of 4

Other databases

Eorzea Database (the official one, on The Lodestone)
Console Games Wiki
Garland Tools (vendors, crafting, drops)