Look att "Uni balls" and you can make something that replaces that and is serviceable.
With two halfs that is holding the center part and two outer screwed in rings.
Otherwise you can do spherical milling with a bit of a weird setup like this.

What you need to consider is offsetting it below the surface and go in with a smaller tool, then cutting half of the hemispherical "groove" on each side.
A form tool in a lathe could maybe work as well.
This how i did the first tests for this;

That resulted in a "receiver cup"

It really helps to make some drawings on either paper or in cad.