This looks vaguely like a pattern I used where first you knit and graft a cable, then pick up edge stitches and do ribbing, then pick up the other edge's stitches and making decreases like a regular hat. See how the cable is sideways but the ribbing is vertical? The kind of cable wouldn't matter, just so you had a comfortable fit at the bottom and could pick up enough stitches for ribbing.
You could also do the whole thing in one big piece with a provisional cast-on, work about an inch and a half of garter stitch on what would be the bottom edge, then do short rows for the crown. That way one big grafted seam would take care of everything and it would all be done at once.