I don't know what Hern does; best to contact them for a definitive answer.
In the beginning, the old guys cast their barrels with cores (the term for the piece that makes the hole.) They always had problems with the cores shifting during the pour; sometimes they would put wires at the inside end to help keep the core in position and the wires would become part of the barrel. Once someone figured out how to drill the bores, casting solid became the universally accepted method with post-casting drilling of the bore. Both straightness and surface finish are better with a drilled-from-solid bore.
Consider that the original M1861 barrels were made in a factory situation where many of the same thing were being made. Consequently, they would have specialized machines and jigs and fixtures to maximize the ease of doing the work. Making one at a time now doesn't justify making all of the fixtures so it would be better to make alterations of the casting by including, for example, holding points that would allow the use of a standard engine lathe for the drilling/boring process, yet they could be ground off in the finishing process after they were no longer needed.
The easiest way to get a M1861 mortar is to throw money at it. Doing it yourself requires a big lathe at a minimum (it could be all done on a big lathe.) I think in one of the previous posts on this subject, I guessed that you would need at least a 25" swing lathe to make a 10" M1861 (and a hoist of some kind to move the casting.) The machining processes are actually pretty simple and few in number but would take a while because of the size of the casting.