Not quite what you are looking for (the user interface is slightly different), but there is an extension to the full calendar plugin that supports recurring events. See Demo here: http://fullcalendar.vinsol.com/
Please note that the code is Ruby on Rails.
I think it may be difficult for you to find a pure javascript plugin for this function, mainly because, although this is not essential, it requires some kind of database code / backend to handle events. Pure javascript solutions to the problem, such as repeating events, are likely to be a bit hacky.
Full calendar control is a great javascript control that extends easily. If you have something like this, then adding a recurring event screen really shouldn't be that big. Most calendar controls there will already pop up when an event is created. The markup / js for the screenshot in your question is really not difficult to write. The backend code is where you end up doing most of your work, I think jQuery plugins won't help you with that.