The pattern below produces a neckwrap that is knit in the round, laid flat, and buttoned at the bottom. The stitch I used is the first half of the stitch pattern Stacey used for her "My So-Called Scarf." There's an excellent tutorial for this stitch pattern on the Mason-Dixon Knitting blog. However, I hope that you will find my version of the stitch fairly simple and won't need the tutorial.
Materials: Karabella Margrite Bulky, (80% Extrafine Merino Wool, 20% Cashmere) 50 g. (1.75 0z.), 71 meters (77 yards), about 1.5 balls per neckwrap.
Circular needle, size 15 (10 mm), 16" long. Substitutes: dpns, two circulars, a long circular for magic loop or any other means of knitting in the round. A smaller size needle can be substituted, but you might need to cast on more stitches. (I used size 15 because that is what I had in a short circular.)
Finished measurements: 4.5" wide x 24" long
SKYOP - Slip one stitch knitwise, knit the next stitch, pass the yarn over the top of the needle and, using the left needle, pass the slipped stitch over both the knitted stitch and the yarn over.
Gauge: 7 SKYOP, 16 rows, in pattern/4 inches (or 14 stitches, 16 rows if you prefer to count a plain knit row)
Instructions: Cast on an odd number of stitches, using a provisional cast on. I cast on 31 stitches for the gray Smilla, and 29 for the brown one. Both worked well. For a provisional cast on, I use a crochet cast on and pick up stitches through the bumps on the back of the crochet chain, but any cast on that can be removed to leave you with loose stitches for a 3-needle bind-off will do.
Round 1: K1, SKYOP around.
Round 2: Knit all stitches.
Round 3: SKYOP until one stitch remains, K1.
Round 4: Knit all stitches.
Note: It is important that you start round 3 with a K1 and that you keep the same stitch count. The pair of stitches that you passed a stitch over on round 1 should be split in round 3. This is what makes the stitches spiral around. If you lose a stitch (which is easy to do if you forget a yarn over) or start every round with a knit stitch, the SKYOP stitches will stack on top of each other, leaving gaps between them.
Repeat Rounds 1-4 until neckwrap is desired length. I suggest 23 to 26", depending on the size neck you'd like to wrap. Add buttonholes as desired when the wrap is two inches shorter than desired length. See buttonhole note below. After making buttonholes (or not), continue in pattern until the piece is the desired length, ending with Round 1 or 3. Divide the stitches equally on two needles and, using a third needle, bind off with a three needle bind off. (You will have one extra stitch; just bind it off by knitting it together with another stitch.) Remove the provisional cast on, place the stitches on two needles and bind off with a three needle bind off.
Buttonholes: For this gray version, I made buttonholes by binding off one stitch and casting on one in the same place on the following row, placing four of these bound-off stitches evenly around the neckwarmer. I then matched up two of the stitches on the front and back to make two buttonholes. However, since the stitch gauge is very large, these buttonholes were too big. I crocheted around them to tighten them up--hand sewing around them in buttonhole stitch would work as well.
The smaller buttons I have for the brown version will button through the stitches, since they are knit at such a loose gauge. No buttonhole is needed. Check your buttons before you get within 2" of the end to see if you need buttonholes.
(Edited to clarify the alternating stitches and needle requirements.)