The finish on this tall oak mirror will be shellac. While the unit could be stained and coated with polyurethane, I like the way that shellac shows off the color and detail of the oak.
There are numerous methods for applying shellac, which we covered thoroughly in Shellac Finishes. We used five coats of shellac with a light sanding in between each coat, and we were left with a beautiful satin finish that really shows off the color and grain of the oak.
After finishing the front and back of the tall oak mirror frame and allowing the shellac ample time to dry thoroughly, place the unit face down onto your woodworking table. Use a bed sheet or some other clean cloths to protect the finish on the front of the frame.
Place the mirror into the rabbet and then attach the plywood back to the frame with some 3/4" long, #6 wood screws.
Finally, attach your mounting bracket of choice onto the top rail of the frame and mount your mirror into position on your wall.