Using 4mm needles and DK wool (I used sirdar escape for a gentle colour change...
Cast on 20
rows 1-5 - K5, P5, K5, P5
rows 6-11 - P5, K5, P5, K5
rows 12-17 - K5, P5, K5, P5
repeat rows 6-17
On row 29, cast off as you go until you get to the last stitch....
Instead of pulling yarn through this one stitch now becomes your crochet stitch. Transfer the remaining stitch from the knitting needle to a 3.5mm crochet needle. Single crochet (UK) in each stitch around the 4 edges of the coaster.
And there you go. Beautifully textured, but bizarrely simples! You might wish to block it out to 4.25" x 4.25" or keep it with a bit of tiny rustic curl.