I think it started as a hood, but it grew longer because nobles wanted to show everyone they could afford the extra fabric, which was expensive, and eventually they started piling it up on the head because the hood tip was getting so long it was in the way, and you eventually ended up with that thing in the picture.

Or I'm way off, and this is not the hat I was thinking about 🤷

I always imagined this portrait was made right after Euler washed his hair, and it's just a towel.

He's at a stag do, they all have to wear their underwear on their heads and line up to do tequila shots out of the strippers cleavage