The phonon modes of individual ultrathin CdSe nanoplatelets are investigated using surface-enhanced Raman scattering in a tightly confined plasmonic geometry. The surface-enhanced Raman scattering spectra, taken on single nanoplatelets sandwiched between a gold nanoparticle and a gold surface, reveal a phonon doublet arising from oscillations perpendicular to and within the platelet plane. The out-of-plane mode cannot be observed with conventional Raman spectroscopy. The resulting strong electric field enhancements and the field vector reorientation within such nanometer-sized plasmonic gaps reveal otherwise hidden information deep into the Brillouin zone illuminating the vibrational properties of ultrathin materials.