Jonathan,
I'm no pro but, I cut the majority of my crowns flat with no recess. I normally use an extremely sharp solid carbide boring bar with a small radius on the cutting tip. I cut them at 1000 rpm and make light cuts from the bore out. I have cut recessed crowns using this method, just set the compound to whatever angle you want, 45 degrees normally for me. Use a Q-tip to slide into the bore and remove looking for any strands pulling from the Q-tip indicating burrs. Repeat until the Q-tip comes out clean.
Hope this helps,
Med.