Okay...am I taking crazy pills!?

[Saseal]

I have one of those o_O I don't remember where exactly I picked that up from, though.... it's just sort of been sitting on a retainer for a while....

http://xivdb.com/?item/2833/Aetherial-Cavalier%27s-Hat

Unfortunately it deosn't say where the Aetherial version is from (but I also used to run Hullbreaker and Stone Vigil HM a lot before the new dungeons... so maybe one of those?) but the non-aetherial (or aka Woolen Cavalier) was from the 'Lady of the Vortex' quest.
http://xivdb.com/?item/2832/Woolen-Cavalier%27s-Hat

Lastly - one easier to get, but slightly different (not sure if the icon appearances actually differ from the wearing appearance) is the plundered Cavalier's (lvl 15) hat from Tam Tara (NM) / Sastasha (NM) / Copperbell (NM)
http://xivdb.com/?item/2679/Plundered-Cavalier%27s-Hat


Edit: oop, I was slow x.x