I think the figure you mean, who is apparently wearing a surplice and a cowl (?) and no wimple, is a little odd, but is not a woman. As tomjaw says, the women in this picture are the figures higher up on the left: they are dressed as nuns.

(Google showed that) This is XV century Flemish book of hours, currently in the Getty in LA. But I think fifteenth-century Flanders is the wrong place and time for double monasteries.

That said, the question remains, who wears that kind of vestments in choir?

I agree with Hawkins here; it looks like female headgear.

Consecrated Virgins used to have the Office of chanting the psalm after the reading during Mass. in Medieval times Consecrated Virgins were primarily religious nuns who received the consecration. They were also permitted to wear the maniple while fulfilling their office.

Scandalous, I know.

So finally I think this garment is a form of the “almuce” (almutium) which has been more like a hood, more like a cope, and sometimes no more than a symbol of (canonical) office, over the centuries.

Here is an (19th c) image of a (14th c) canon wearing exactly the same head covering.

Here is another, I think taken from a brass.

Other reasons the figures cannot be a women, as proposed: these people are all wearing essentially the same vestments, except for the head covering, but women and men dressed differently from each other all the time in the 15th century; people did not sit in choir in the 15 c in mixed groups; these people are not in ordinary clothes and must vest for the ceremony, but there are no women's vestries.

I think we need to remember that chanting the office in a big medieval church in the dead of winter without modern hearing aids would have been a frigid affair, to say the least. These head coverings were likely borne out of a very practical solution to a very real problem. At least, that’s my bet.

err not only that

The surplice itself is meant to be worn over furs. That's what it means. Superpelliceum literally means that! In modern times, I've seen a priest wear his puffy vest with a surplice. It's awkward but necessary.

I do not have one...but that might be fun. St. Aelred is a very medieval Ordinariate parish aesthetically, so it wouldn't be out of place. Certainly would be quirky...

Just think St John Fisher instead.
https://upload.wikimedia.org/wikipedia/commons/thumb/1/1c/San_Juan_Fisher_Obispo_de_Rochester_y_Mártir.jpg/185px-San_Juan_Fisher_Obispo_de_Rochester_y_Mártir.jpg