As far as I can tell, there’s no way to do that “out of the box”, and the only way to do it that I know of is still only a 99% solution.
And also involves installing extra software and setting up an account on a website. Normally, that would be a “Hell, no” for me, but curiosity overcame caution.
The website is Wowhead. The extra software is the Wowhead Client, which interacts with an WoW addon which is part of the Client package to record the things you loot, the critters you kill, the crafting recipes you learn, and the quests/achievements you accomplish. Somehow, this has access to the “deep” quest history of your character, even before you installed the addon, so this qualifies as a potential solution.
This is my main’s page at Wowhead. (Ignore the awful gear.) Select the “Quests” tab and you’ll see bar graphs depicting percentage completion of quests in various categories, and gosh there are a lot of quests. Click one of the bar graphs–say, “Northrend”–and you’ll see below lists of zones within Northrend and progress counts within the zones. Click one of the zones and you’ll get a display of quests completed and not completed.
It’s fairly powerful, but (A) requires an account at Wowhead, and (B) requires the Wowhead Client software with associated addon. And also, (C), Wowhead is datamining your activity to keep their own databases fresh, so if you kill Puppywuppy the rare elite puppy while the Wowhead addon is running, the fact you killed it at a certain place at a certain time goes into their database, as well as the loot you took from it.
Kinda Big Brother. But having this kind of visibility into my own characters is cool. YMMV.
I mentioned a “99%” solution. If you look at the quest counter page, you’ll see a legend saying “Note: Certain quests aren’t tracked by Blizzard’s API.” The word “Certain” means “repeatable quests and quests that don’t appear in your quest log”. There are a few of them, but I don’t recall being especially noteworthy.