I suggest you mill the spherical surface. With the milling cutter axis normal to the workpiece's axis, if the workpiece is rotated, a 'hollow' rotating cutter – or a single-point tool – will produce a sperical surface. (This is because any slice through a sphere is a disk.)
In this case, the cutter diameter has to be the distance between the shoulders. The cutter's form (in this case) has to be hollow, internally bevelled, with effectively end-cutting teeth. Think of a 'solid of rotation' formed generated by a tool like the one on the left of Jason's sketch, or think of a hole saw, with its teeth tapered so it gets as far into the aforementioned corner as is required; a single-point tool works also, of course. The workpiece is slowly rotated as the cutter is fed radially. Perhaps a good idea to remove the bulk of the material with a more hefty cutter – you can use a single-point cutter in a boring head. Milling spherical surfaces is fun, and a good talking point…
This idea, with a little elaboration, is really neat for things like 3-ball handles.