Basic Information
A besagew was a circular (or at least vaguely circular) piece of plate armour that fitted onto the upper chest area of a breastplate or cuirass to protect the shoulder-joint from the front by covering the gap between breastplate and pauldron. This was an alternative to the gardbrace, but could be worn at the same time as a full pauldron. Or not. Although it can be difficult to prove if a given suit that has survived from historical times was designed to have them or not as they are relatively easy bits to lose.
These are very much creatures of the full plate era, although their role is fulfilled in some preceeding designs (such as plate mail) by pieces called aillettes ("little wings") - although these can just as easily have been meant to serve as an extension of the pauldron down the outer arm instead and weren't always made of metal.
The besagew may also be called a roundel or rondel, although this technically refers to any round piece of armour.