The notion of spontaneous symmetry breaking has been used to describe phase transitions in a variety of physical systems. In crystalline solids, the breaking of certain symmetries, such as mirror symmetry, is difficult to detect unambiguously. Using 1$T$-TaS$_2$, we demonstrate here that rotational-anisotropy second harmonic generation (RA-SHG) is not only a sensitive technique for the detection of broken mirror symmetry, but also that it can differentiate between mirror symmetry-broken structures of opposite planar chirality. We also show that our analysis is applicable to a wide class of different materials with mirror symmetry-breaking transitions. Lastly, we find evidence for bulk mirror symmetry-breaking in the incommensurate charge density wave phase of 1$T$-TaS$_2$. Our results pave the way for RA-SHG to probe candidate materials where broken mirror symmetry may play a pivotal role.