This widely used full-deck false shuffle was first described in print by G. W. Hunter in The Magazine of Magic, Vol. 7 No. 4, Mar. 1920, p. 81. It is interesting to note that Hunter doesn't seem to claim it. He writes, “The two shuffles that I am about to describe are easily learnt. They are almost unknown, and have not hitherto appeared in print”.
A precursor to this shuffle—one that uses the repeat overhand-shuffle feature of genuinely mixing the cards, and then undoing that mixing—is a technique by Slygo (John T. Halloran) detailed in The Sphinx, Vol. 9 No. 4, June 1910, p. 90. It's the same concept as the shuffle described by Hunter, but the runs of single cards occur at the beginning of the first shuffle (reversing their order) and at the end of the second shuffle (reinstating the original order), rather than running cards in the middle of the deck.
Some notable additions to this concept include Bob Fisher's “A False Shuffle That Really Shuffles” in The Sphinx, Vol. 31 No. 4, June 1932, p. 147, “The Gordon Bruce False Shuffle” in Gordon Bruce's Lecture Notes, 1985, n.p. (and later in Five Times Five Scotland, 1998, p. 16), and Justin Hanes's “Moses” in Mystery Engineering, 2004, n.p.