A Pasty (pronounced PAS-tee) is a mixture of meat and potatoes, sealed into a pastry crust, making it a self-contained sandwich.
The pasty originated in Cornwall where it was prepared by Cornish housewives and favored in the miner's lunch bucket. The pastry-wrapped meal was wrapped into an airtight waterproof oilcloth package and placed in a small steel churn which was then filled with hot tea. Down in the mines, the churns were placed next to the fires at the vent shafts which forced the air upwards to circulate fresh air around the mine. These fires kept the churn and all its contents hot for mealtime. The pasty would have an X on one side to mark where to start eating it --- the latter end had a little partition inside which was filled with apples, or peaches, cinnamon and sugar to add dessert to the meal. A thin but larger slice of potato was used to separate the ingredients of the pasty.
Source: http://www.sihope.com/~tipi/
Pasties appear to have come to the USA via Butte, Montana. If you aren't close to any significant mining operations, you probably have never heard of them, and instead think these are the things glued onto a stripper's breasts. For what it is worth, I've never heard of a pasty with built-in dessert...
Compare with a krautburger or Runza, which replaces the potatoes with cabbage.
Oh... er... by the way, since nobody else has mentioned it, a pasty is a self-adhesive adornment for the female breast, usually worn by adult entertainers -- strippers. It is designed to cover the areola in communities where the showing of the areola is considered vulgar.
Different communities have different legislation on the Adult Entertainment business. In Arizona, topless dancers must put clear liquid latex over their nipples. In other communities, pasties are the norm along with a lock or anchor -- a strip of adhesive tape from the bottom of the areola to the bottom of the breast.
I feel silly admitting it, but I am having a really tough time researching this... Who'd have thought putting 'breasts stripper pasties' into Google would turn up so much?!