I am almost sure that it was someone making a coin similar to a magician's double headed or double tailed coins. The key is to use a lathe or mill to machine out the one side of the coin exactly on the inside edge of the rim leaving the "cup" you mention. Then another coin is machined to remove the same area, leaving just the obverse from the inside edge of the rim. If you are good, the "cut" will be nearly invisible in the shadow of the rim when you put them together. And as said above you could change one side to produce a "mule" of sorts. Look for 1958 cents with memorial backs and 1959 cents with wheat backs.
Jim
