Azare's Plane is a single map zone with no neighbors, which can be reached by Dimension Traveling to yellow.
Scattered throughout the zone are many pools of strange liquid, one for every potion type in the game. A visitor can fill their empty vials with any potion type they wish.
The liquid pools are labeled using their unidentified names (murky, bubbling, etc), even if the resulting potion is known. Players that wish to prepare for a later visit to Azare's Plane are advised to keep track of potion adjectives outside of the game as they progress.
There are really only two ways to "farm" additional empty vials: wishing for them in amounts equal to your Luck, and spamming scrolls of wonder. Note that the wonder method may have a wide variety of side effects; the user should be prepared by wielding a wand of restoration in case of a bad polymorph, and using it in a zone that you don't mind ruining with mud, and doesn't have unclaimed items lying around.