The target normal single-spin asymmetry in electron nucleon scattering is studied in the framework of the $1/N_c$ expansion of QCD, which allows for a rigorous description in the energy range that includes the $\Delta$ resonance and below the second baryon resonance region. The asymmetry is driven by the absorptive part of the two-photon exchange component of the scattering amplitude, being therefore the most unambiguous two-photon exchange effect. Such amplitude is shown to be described up to the next to leading order in the $1/N_c$ expansion only in terms of the charge and magnetic form factors of the nucleons, consequence of the approximate $SU(4)$ spin flavor symmetry valid in the large $N_c$ limit for baryons. A discussion is provided of the $1/N_c$ expansion framework along with the results for the asymmetries in elastic ($e^- N^{\uparrow}\to e^- N$), inelastic ($e^- N^{\uparrow}\to e^- \Delta$), and inclusive scattering.