Highly Curved Parabolic Makeup Mirror?
If your objective is not limited to locating a vanity mirror of this sort (I failed to do so), you may discover that your objective can be gained by searching for parabolic trough reflector or parabolic trough mirror. The returns I found from those terms cover mostly solar collectors designed to focus light on thermally related energy systems. Some of the links also point to engineering documents regarding design and construction.

An advantage of such a design in thermal energy collection is that it can be aligned in one direction and rotated on the long axis to provide near-continuous exposure to the sun.