It is the darker pork, sliced or coarse chopped with no large chunks of fat. Yep - I don't like the bun falling apart either.Please describe a "lean brown"...
Personally I prefer the slaw on the side but I can eat it on the BBQ sandwich if it does not make the bun too soggy...!
As simple as it may sound, I occasionally like a fried pork chop sandwich with Miracle Whip, sliced tomatoes and onion, on toast or a bun.