The idea of passing or slipping a single card from the top to the bottom of the deck is centuries old. An early example of this sleight at the gaming table appeared in L’Antidote ou le contrepoison des chevaliers d’industrie, 1768, p. 76 of the Pieper translation. This book was translated in Gibecière, Vol. 7 No. 2, Summer 2012, p. 60-175. The One-Card Middle Pass is of similar vintage, and is probably accidentally rediscovered by every magician while attempting to master the standard Pass. Victor Farelli, in Farelli's Card Magic, Part Two, 1933, p. 63, mentions that John Henry Anderson used this sleight, which would probably be in the mid-1800s. Farelli credits the sleight to Anderson, but this seems incautious. The sleight must predate Anderson, as suggested by the following entry by Henri Decremp.
It is a small step from slipping the top card to the bottom to reversing it along the way, revolving it face up around the side of the deck. This may be considered the original method for the Half Pass. It was also done with a portion of the deck. An early description of this–perhaps the first–is given in the context of a Card at Any Number effect, described by Henri Decremp in Le Testament de Jérôme Sharp, 1785, p. 161 of the Hugard translation (unpublished).
There is also a variant of the move, done while passing-slipping a single card from the center to the bottom, in which the card is rotated around the lower packet to a reversed condition on the bottom. W. G. Craigen describes this in “A 'Sleight' Improvement” in The Magic Wand, Vol. 18 No. 142, June-Sep. 1929, p. 66. The “improvement” he was referring to is the use of this one move in place of needing two moves to accomplish a reversed-card effect by Verrall Wass: the traditional Pass followed by the original version of the Half Pass mentioned above. Craigen concludes by writing: “I don't for one moment suppose that this 'Sleight' Improvement is original, but I have never seen it described in print or known it to be used by any other conjurer.” Indeed, in commenting on this item in the next issue of the same journal (Oct-Nov. 1929, p. 118), Verrall Wass writes that “Mr. Craigen's method is already known to me.” The origin of all these single-card passes and pass reversals likely goes back centuries.