It takes small flap/disk sanders, lots of flaps/disks, and lots of time. Just taking off the high spots takes 10-15 minutes. A mirror finish requires working through progressively finer polishing compounds and can be quite time consuming, particularly in the spots harder to reach with power/pneumatic tools (like the transition between the base of the pan and the walls).

Edit: Given the text on the site, it appears this is a single individual craftsman polishing those pans, which likely also contributes.