Most engravers will not touch a casehardened frame once it's done. You'll need to have the engraving done before any casehardening is applied.
Casehardening is applied by packing the metal part in a canister of bone meal, charcoal, or whatever the smith uses. The whole thing is packed into a oven, and brought to a pretty high temperature. A high temp oven is required, and some folks have found that old potter's ovens work well.
When the part reaches temperature, it is removed, and submersed in liquid, often with oil on top. The swirling patterns you see are created based on how each smith does his quenching, and what pack material he uses.
This isn't a job an amateur could or should do. Many good gunsmiths wont even try it. Turnbulls is about the best, but there are others who do excellent work, and charge much less. Classic Arms and Gun Fancy both do great work.
Dale Woody, at Gun Fancy did the engraving and casehardening on my Hepburn, and IMO the workmanship is excellent. His prices are most reasonable.
http://www.gunfancy.com/