Over at String or Nothing, Kim’s talking about making a heel-flap heel (as opposed to i.e. a short-row heel) on toe-up socks. She’s having issues with it, and has posted at length. This makes me wonder whether it can possibly be as simple as I’m imagining it.
Make your toe as usual, knit to about where the arch of the instep starts rising, increase two every other round on either “edge” of the foot till you’ve done 1/4 your base number of stitches (64 for me, usually, so 16) on each side. Start knitting back and forth, centered over the back heel on 1/4+2 of your base, increasing one stitch at each end of each row and catching one of your live stitches likewise, till you have 1/2 your base number on the heel needles. Then knit back and forth, still catching a live stitch on each row, till the instep needle has 1/2 your base number on it and switch back to working in the round.
It’s pretty much an exact reversal of the Dutch heel that many people learn for top-down socks. Am I oversimplifying?