Green tater:
Extraordinary (distinguished, dignified, acclaimed)
Now the perennial question, I think, is whether something is extraordinary in a qualitative way aka. that there is nothing like it in principle, or whether it is "only" extraordinary quantitatively aka. there are things like it, but it is just a noch more of whatever it is.
Thinking of that I would say that the Void and the Music of the Ainur are on a class of their own with "extraordinariness".
Now some might think the Girdle of Melian could give them some competition. I mean it's not the nature of forests to lose you as such. If you get lost in a normal forest it is you who are stupid (or bad in orienteering), but the forest doesn't actively make you lose your direction. But... and the obvious counterargument to Melian's Girdle would be that also other forests in the ME seem to be both able and willing to do just that. So the Girdle of Melian maybe was extraordinary in being better in that than the Old Forest, The Fangorn, the Mirkwood, but it was only better at doing a thing others did too.
Like Lembas is better keeping hunger away than other foods which also keep hunger at bay - or Mithril that protects you more with lesser weight and brighter shine than other mail but still does the same thing... and you can see where the argument goes from here if we consider Thuringwethil, Isildur, Arwen, Gondolin or the Green Dragon... although with the latter five you could actually make an argument there were better examples than those named in their specific doings... Like Luthien giving nice competition to Arwen, Prancing Pony competing the Green Dragon, Armenelos competing Gondolin in grandeur or Menegroth in secrecy, Carcaroth competing with Thuringwethil, any great hero of old "out-heroing" Isildur...
Many of those points sure are open to argument. But that's exactly the point: the fact that you can argue whether Aragorn was a more distinguished or acclaimed hero than Isildur, or whether one should consider Beren as still more extraordinary, proves the point them being not extraordinary in quality but only in quantity.
How could one argue the relative extraordinariness of "being itself" or "not-being" in regards to something else, like a teapot, Minas Tirith or Helcaraxë?
No way. You don't compare "coming-in-to-being" or "existing" or "non-existence" or "void" with anything. Like Immanuel Kant said: existence is not a predicate you can attribute to something, but it is the condition via which some thing can have an attribute in the fiorst place: if something doesn't exist it can't be blue, white, mushy or lovable... existence comes first, then qualities an existant being can have. like heroism, being able to delay hunger, protecting you from blades or arrows, making you lost etc.
But you can possibly at some level compare existence and non-existence against each other as the primordial issues...
Most religions start with the obvious state of nothingness (like in Judaism, Christianity and Islam) often described as a void (fex. in Scandinavian and Babylonian mythologies). Then comes the extraordinary thing: creation!
And the thing is quite clear in our everyday speech as well: we talk of the "miracle of birth" and the "naturalness of death" ("nothing in this life can be trusted but taxes and death"
).
So: why is there something rather than nothing? That is the extraordinary thing!