🙂 Cute the way you describe it. The “dark circular cap” is either a hat or a dark tichel that is set in a way to look like a “cap”.
It can be worn on either a sheitel (with some of it protruding from the sides) or with a shpitzel (in which case you will only see it in the front.
You will find it in Viznitz and Satmar, and I’m sure in plenty other chassidus…