And no, it’s not Brother Cadfael, for anyone about to say that based on my title alone.
Read it about 10 years ago. Set some time in the early middle ages - about AD 900 or so - in Britain. The main character/investigator is a woman of some religious order - possibly Irish or Welsh, some religious background slightly non-mainstream from a Catholic point of view. There is at least one murder. Can’t remember anything more.
Ring any bells, anyone?