How to glue together this stone-like material?
The porosity of the material as it appears in the photo would have one aiming for an adhesive with some viscosity. You could have a solid and clean bond with a gel-type super glue. I've recently repaired a similarly irregular break of a less porous substance with Loctite brand gel. It does not seep too deeply into the material, but enough to get a "grip." Any brand of similar gel super glues would work.

Alternatively, a reasonably thick epoxy would accomplish a good bond. Having a break of this nature where the opposing surfaces mate nearly exactly allows for greater surface area, meaning better bond.

I reference the epoxy and gel super glues because I've had good luck in the last few days with both types.

Another option is the "goop" type product line, but it's too thick, in my opinion and might not bond into the porous surface as well. Somewhat unsightly at the edges, too.

The super glue option will give less obvious joins, and the epoxy falls in the middle.