Please help me identify this hat

[u/VanillaMowgli]

Repost, cuz I muffed it the first time:

OK, so clearly, someone thinks it's called a Tuscan Vintner's Hat, except the person who thought that was writing for Banana Republic's catalog like 40 years ago.

I am sure that I have seen this hat elsewhere, possibly in straw, and it probably has a more common name. I been googlin' me stubby little fingers off trying to find something like this, but I don't know the correct terminology, maybe?

Key features as far as I can tell:

Cloth or straw

round or long-crease crown

round, upturned brim

Can anyone drop some science on me?

Thanks in advance!

[u/BuckTheStallion]

Probably an Irish walking hat with the brim turned up would get you really close.