A beanie with a bill is a variation of the traditional knit beanie incorporating a hard plastic mold sewn into the knit to form a baseball cap-like bill. The bill variation was developed for extreme sports athletes who wanted the look of a beanie, but needed protection from the sun.
The word "beanie" comes from the word "toque" which is what chef's style hats were called in Europe in the early 1900s. In the current market there are many variations of the bill, including bills that look like baseball caps, military-style caps, and bills specifically for snowboarders. They are sold at places ranging from convenience stores to high fashion flagship stores.