"Witch Milking the Handle of an Axe", from Dr. Johannes Geiler vons Keisersperg, "Die Emeis" (Strausborg, 1517), reproduced as plate 156 (pg. 183) in Emile Grillot de Givry's "Anthology of Sorcery, Magic and Alchemy". Such a notion as taking this halfway seriously may be a thorn in the side of some modern witches, but such feats of manifestion are part and parcel of pretty much every spiritual tradition one cares to name.
The exception would be that the evil portrayal of the witch should of course rank as the kind of satyrical, backwards travesty that is so common in much older literature; it's more likely that such persons well trained in various arts, as were many whom Blavatsky refers to, may have quietly been boons to their communities through such magickal feats- much as they were often valuable midwives and natural healers.
The woodcut may contain valuable clues to the process, which may be aided, like much magick, by heat, and other materials; the wooden post in which the axeblade is stuck may be a candidate for containing vitriol. Whether the alchemists wish to debate whether this, like so many of their materials is literal or figurative, a borderline magnetic material such as vitriol might well be a participant in such an operation. Magnetism, of course, seems to pertain to many accoutrements of occultists throughout the ages, as many pages at this site will attest.
Our own modern efforts to recreate organic molecules from primordial mixtures of simple materials like methane and ammonia, as we expect the beginning of life occured, produce the building blocks of proteins and require very little guidance in order to do so. In truth, this is one of the simplest possible materializations imaginable, and one might easily produce today.
The theme of milking or stoking an object for a magickal purpose is also certainly far from unheard of; we can even extend such a notion to being the same as the rubbing of Alladin's lamp, and if we wish to observe that such an act may dabble in triboelectricity, or electricity from friction, much as the sacred hides worn by ancient preists, more power to us.
The comical theme that constantly accompanies these many, many anecdotes of this feat, that the milk is actually magickally stolen by being teleported from other people's cows, may have the legitimate value that we are alerted that the milk may not materialize out of virtually nothing, but may have to acquire matter at a distance- not from the neighbor's cows, but from the ground.
The peculiar detail that is many accounts, namely that the milk produced magickally is blue in color, may provide other valuable clues if taken seriously; it may imply certain floral pigments are at use within the operation, as may be so with much ancient Egyptian magick.
Some of the tone of ancient renditions of Tutankhamen's nebris , which may be the "grandfather of witches's brooms", imply this may be one of a number of miracles it was designed to perform, and the possibility they are powered by the pigments of certain plants, such as the cornflower and the Egyptian blue water lily, is hard or impossible to escape.
Should anyone be still at a loss for mechanisms here how this may be happening, hopefully a visit to the Ectoplasm and Alchemy page and other pages at this site, will better equip them with tools of speculation and possible explanation.
The feats that many occultists and scientific devices alike are well known for, are no less incredible, and may well be little different whatsoever from the miracle in question here.