Shadow problem on character

Hi everyone, I have a problem with the shadow of the hat on one of my characters.
Light seems to bleed through the part of the hat that is closest to the head, resulting in a strange ring without shadows.

I tried changing light settings like shadow bias and Cascaded Shadows but most of them seem to only influence static light not the dynamic light a character needs.

Is there a way to fix this?

The hat is a plane with a two sided material so maybe a mesh with more geometry would help?