That part could be done in either a lathe or mill. I'm going to guess that the OD of the raw stock is about 100mm
For a lathe, a machine like a Haas DS-30Y would work, a horizontal machining center. https://www.haascnc.com/content/haas...ne.DS-30Y.html This would allow running raw stock to finished part in one setup.
It could also be built on a 4 axis mill, but would require two separate operations to complete, a 5 axis would eliminate one setup. The Haas mini would be a good choice. https://www.haascnc.com/machines/ver...ini-mills.html
There are many other machines that would do this job.