Kaufman's Kona Cotton Solids are an example of 'premium broadcloth'. Same for Moda Bella Solids and some, but not all, other solid cottons. Broadcloth is a method of weaving. It dates back to the 1500's in England.
http://en.wikipedia.org/wiki/Broadcloth
Todays cotton broadcloths are generally 60x60 threads, slightly fewer than premium quilting cotton prints. If you'll notice at fabric.com, the premium broadcloths are in the quilting section and the other broadcloths (blends, etc) are in apparel.