I use a .50 cal brass brush with a 2 1/2 x 2 1/2 cleaning patch, I cut from old cotton t-shirt material, wrapped around the brush.
I have my T/C .50 cal barrel in hot water that has a bit of Dawn dish soap added.
I thoroughly wet the cotton patch on the brush and work the brush up and down inside the barrel.
The bristles on the end of the brush deform, allowing the end of the brush & patch to get into the patented breech area, while the rest of the bristles poke through the thin patch to scrub the lands and grooves of the barrel.
Using this method, I have never had any fouling build up in the breech!