As promised, here is the recipe for the "One Day Beret". This will work for any gauge. That's one thing that I love about top down! For the hat in the photo I alternated each round between two colors of handpainted yarn.
To make the hat I cast on 4 sts.
For the first round I knit into the front and back of each stitch. (8sts) Place markers between each of these eight stitches, they will mark your increases.
2nd round: Kf&b each stitch (16 sts).
3rd round: (Kf&B 1, k1) repeat to end of round (24 sts).
(I work the increase rounds for each of the first three rounds to make the top of the hat a little flatter.)
4th round: knit
5th round: (Kf&b, k to marker) repeat to end of round (32 sts)
Continue in this way, alternating plain knit rounds with increase rounds. The number of knit stitches between the kf&b's will increase by 1 each time. Stop increasing once your work measures about 8.5" diameter.
Now work plain stockingette for 3 1/2 to 4". The amount of plain stockinette you work will determine how "slouchy" the hat is.
Begin decreasing by (K2tog, knit to marker) to end of round. Alternate this decrease round with plain knit rounds until the desired number of brim stitches** remain.
**You will determine the desired number of brim stitches "c" by finding your stitches per inch "a" and your head measurement minus 2 inches "b". Now multilply: axb=c.
Adjust this number to the nearest multiple of 8. Since you have already subtracted 2" from the head measurement, when in doubt adjust the number up.
Switch to needles that are 1 size smaller than those that your worked the body of the hat with and work in 1x1 rib for about 1-1.5". Bind off loosely.