But I can't oil it right away because I still have to clean all the black soot away.
After using boiling water and scrubbing with patches, normally the next thing you do is clean with solvent patches until they're not coming out black. The first couple of solvent patches you just push through once. Then scrub with solvent on the next few patches. You'll notice they get cleaner after a few.
If it's really sooty use the bronze brush right after the boiling water. If necessary, use some boiling water, then the brush, then more boiling water. Repeat as required. That's what the brush is for. Follow with solvent patches as above, then a dry patch or two, then lightly oil with your favorite.
You probably won't need to use the brush very often, but it makes short work of breaking soot loose, especially if you've just loosened everything up with boiling water.
As others have pointed out, the boiling water evaporates almost instantly from the steel surfaces. One thing people forget to mention is that it also makes the steel hot. Wear gloves or protect the hand holding the rifle in some way. Much less painful.
Some people claim you shouldn't use the bronze brush in a steel barrel.
Well, 1) bronze is a lot softer than steel, 2) you don't use it every time, and 3) the military forces of the world wouldn't put them in cleaning kits if they were unnecessary, or if they reduced the service life of the rifle.
This method works for me. I have clean, shiny, barrels with bright rifling and no rust after thousands of rounds of corrosive ammo. YMMV.