I have that with a bouncer (znc) and a plugin. I've not used it, but it is my understanding that IRCCloud does this too. Problem is that there aren't many easily usable options for this apart from IRCCloud and even IRCCloud itself isn't all that well marketed.

Always seemed kind of weird how while IRC is full with FOSS people who are willing to use their time on various projects they're not getting paid for, most of whom also seem to worry about IRC dying out, nobody is really doing anything about it. A lot of the conveniences we miss could mostly be solved by making modern clients that are actually good.