A grinding mill or seasoning grinder for grinding seasonings includes a stator and a rotatably mounted rotor having a base body with a shape of a truncated cone, where the rotor concentric to the stator. The stator and the rotor each include milling projections which are, at least in some sections, convexly curved in cross-section and the surfaces of milling projections are devoid of discontinuities that include edges or undercuts.