When I first got into turning I made a number of these. Initially, I used 3" bevel-edged mirrors that I bought from PSI, but I later found that I could get 2" mirrors for a lot less from AC Moore or Michaels. However, because the edges of these were not beveled, I had to be more careful to make sure that the mirrors are fully recessed into the turned surround so that the fingers are protected from that sharp edge; also, it's prudent to leave a small gap around the mirror to allow the wood to expand/contract without contacting the mirror. As noted below, because I wanted a mirror that could easily travel with me, it made sense that the surrounding wood frame be 1/16" or so proud of the surface of the glass to protect it from damage.
The approach I took was to attach a piece of 3/4" timber to a glue block using double-stick tape to turn the basic shape and cut a recess to receive the mirror. Then, I reversed the blank, either using more double-stick tape, or better yet gripping the edge of the recess using chuck jaws in expansion mode, to turn the back. The glass mirror is then attached in that recess using either silicone adhesive or double stick tape; either is flexible enough to withstand any wood movement that might occur. I didn't bother with an overlay frame.
I made a few with handles that became Christmas gifts, but at the time I was using a contact lens and needed to have a small mirror that could travel with me for inserting or removing the lens, and I found that a 2" mirror in a wooden surround (about 2 1/2" outside diameter) without a handle was exactly what was needed for that job. When making the handled version using bevel-edge mirrors, it made sense that the overall thickness be about the same as the diameter of the handle - somewhere around 5/8". But the unhandled versions could be a bit thinner - ultimately, I wanted a back thickness of around 1/8", so if the mirror itself was 1/8", and allowing for that 1/16" setback and about the same for adhesive or mounting tape, the overall thickness was more in the 3/8-1/2" range.
