You would have to put in a dropped section to lower the ceiling line of that nook. You could add tapered runners to make it parallel to the floor, or just add straight stock and drywall to lower it. Of course you will be taping and mudding that drywall dropped ceiling and having a matching issue with the existing ceiling. One other option would be to add a short false beam there. No drywall work at all. Add blocking to the ceiling, slip up a false beam that is bigger than the crown to make a reveal between the beam and the crown, and nail to blocking, then add the crown.