Fluellen, Henry V, Act IV, scene 7 reads...

"Your magesty says very true: if your majestie is remembered of it, the Welshmen did good service in a garden where leeks did grow, wearing leeks in their Monmouth caps; which, your majesty knows, to this hour is an honourable badge of service; and I do believe your majesty takes no scorn to wear the leek upon Saint Davey's day."

Stephen doesn't have a leek in his Monmouth cap because he is not Welsh, but Louise is Welsh, and she has just made a pattern for one in PYF Black Welsh Mountain DK.  
The Welsh town of Monmouth lies on the River Wye, not far from Archenfield, a region noted for it's Ryeland sheep. Ryeland produces wool which is great for felting.  Being near the river for easy distribution, and near the sheep for wool, Monmouth was perfectly situated to become a centre of a knitting industry. 
The industry produced several kinds of knitted goods, but became best known for it's caps, which they couldn't stop making and exported across England and Wales and the continent. The Monmouth Cap was at it's trendiest in 15th and 16th centuries, when we simply adored them. In 1488, Henry VII made the Cappers Act, which imposed a fine for the wearing of foreign- made caps. Why should we wear other caps, when we were so proud of our Monmouth knitters.
 Elizabeth I, in 1571, still loved the caps and made a statue "An Act for the Continuance of the Making of Caps," list 15 crafts related to their production, and it required that "...all males above the age of six, except some of certain state and condition, shall wear upon the Sabbath and Holydays, one cap of wool knit, thicked and dressed in England, upon the forefeiture of 3s 4d...." Wives "were constrained to wear white caps of woolen yarn, unless their husbands were of good value in the Queen's book or could prove themselves gentlemen by descent..."
the Monmouth cap was nearly always brown, with a button on top and a tag to hang it up, but there are some records of them being red.  Ryeland fleeces became much sort after and caps started to be made from other sheep breeds.  They became so fashionable that people started making them everywhere and the term 'Monmouth' refered only to the style, and not to the place of origin. This cap was made at Prick Your Finger in London, and the rest of the information on this fascinating subject, including the Monmouth caps sailing to the new World, can be found in the essay "A Short History of the Monmouth Cap" by Jennifer L.Carlson, from where this whole post was lifted.