The Burkman Brothers use hand woven madras cloth.
The cotton used in the production of madras cloth is called varalashmi and it has a very short staple making it perfect for lightweight shirting. It is also notable as a fabric for the fact that both sides of the cloth look the same.
Get your saturated madras shirt here.
During the 1960's a popular style was called bleeding Madras which was made using dyes that were not colorfast. The results were a garment that would yield a new look with each wash. The Burkman Brothers used a similar technique in making their overdye popover shirt (pictured above).