I've seen these done in one piece and also done as a flat disc with parts added around the rim, usually made of parts that matched the disc grain direction. In either case the carving was, as far as I can tell, achieved by carving in the solid, i.e., if the edge was built up that was done first then the carving and shaping.
I have also seen a couple of examples of someone doing a reproduction where they used a router and patterns to hog out the bulk of the carving, and finishing the crisp detailing with hand tools. I can't recall in detail the nature of the jigs, but there were a few of them made to do the job. In the examples I've either seen, worked on, or repaired over the years the most common way to get the flat surface in the middle as far as I could tell was by turning a large blank on the lathe.
In a contemporary situation where you want to build a copy I see no reason why you shouldn't come up with methods that suit the tools you have, e.g., hogging out the centre with a router and jig if you don't have a lathe that can handle such a large disk, as well as setting up various jigs and router cutters to create the bulk of the pie crust.
Still, if you want something that looks crisp you do have to do handwork to get into the corners because the modern copies I've seen with sludgy corners and the like where the machine tools couldn't reach properly I think tend to look generally a bit naff. Slainte.