Personally, I find this menu in a menu solution irritating. It comes with some inherent missed-click risk that could lead to accidental menu abandonment. It’s something worth testing, but I'd have another option to run it against.
I hate to critique other answers in an answer but ...
Drop in panel to modal pop up is far worse. You’re making the user jump around too much.
For scenarios like this, I’ve had good luck with sliding panels. It keeps the user’s focus in a tidy little space and adds a friendly animation into what might otherwise be a ho hum experience.
For those who haven’t used sliding panels, allow me to illustrate:
It just occurred to me that I left out one small but important flow detail. When the user makes their selection in the second panel, slide them back to the first and change the thing they took action on to confirm. It’s also nice to provide a mechanism to undo or configure properties of that action. I'll add to the image if I get a chance today.