I was aware of 'slip casting', like this:
... but the shape you want requires a mold in contact with both major surfaces.
... which you could do, not with injection molding, but with something more like compression molding or transfer molding.
Note that slip casting molds have to be porous in order to extract the water. I think the pores get clogged with fines, so the molds have to be discarded after a few cycles.
If a sheet of wet clay were compressed between a couple of shiny hard nonporous forms, each in a 'C' shape, some clay would be squeezed out of the substantial gaps around the edges. At which point the excess could be manually torn off, leaving a rough edge, roughly in the shape of a baseball's seam. If the pressure were maintained for a while, some liquid water might also find its way to the gaps, allowing the clay to become more dense, and possibly withstand handling after the molds were gently separated.
That's how I'd try to do it, if I couldn't buy the tooling, but that's all conjecture.
You probably don't want to make just a few, so you need an automated process. Somebody must make machines to form, e.g. porcelain insulators for guy wires and such, which are topologically similar and must be mass produced.
Mike Halloran
Pembroke Pines, FL, USA