Personally, I don't find the look of the standard tiara appealing, but it is the most commonly-attested headwear for Persians in Greece, and is very easy to make at home.
A tiara pattern for a large head, with moderate-length neck flap (left).
If you choose felt, all you need to do is cut out the "blank," stitch up the front seam and turn the hat inside-out.
If you choose felt, all you need to do is cut out the "blank," stitch up the front seam and turn the hat inside-out.
Persians appear to have sometimes worn tiaras tied around the crown with a cord of some kind. On this practice run, I'm just using a bit of leftover cotton belting.
If you don't like the look of the long earflaps, they may be tied up Cappadocian-style, like a modern hunting cap or ushanka.
For an even tidier look, the flaps can be tucked into themselves.
From the back.
I'm going to have to rescind my words about the fabric needing to be soft enough for the peak to lay to one side. It appears that even the very soft polyester felt I used on this prototype isn't flimsy enough for that purpose. I'd guess that the flopped-over look was probably achieved using a fine woven cloth, either wool or linen.
Again, for the Graeco-Persian wars, I have only heard of felt being used. Greek art typically shows Persian (or possibly Scythian, etc.) soldiers wearing tiaras with rather stiff-looking peaks that are often curled, but not flopped, forward. So it's possible that the stiff peak is okay for our purposes.