I'd suggest using buckram or even Fosshape. I've never made a hat before though, so I can't recommend a pattern for that particular shape.
Fayt Leingod - Star Ocean:Till the End of Time - 85% finished
Morrigan (Winter Palace) - Dragon Age: Inquisition - 5% finished
Fidel Camus - Star Ocean: Integrity and Faithlessness - on hold
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