The resonance wavelength of a coupled plasmonic system is extremely sensitive to the distance between its metallic surfaces, resulting in "plasmon rulers". We explore this behavior in the subnanometer regime using self-assembled monolayers of bis-phthalocyanine molecules in a nanoparticle-on-mirror (NPoM) construct. These allow unprecedented subangstrom control over spacer thickness via choice of metal center, in a gap-size regime at the quantum-mechanical limit of plasmonic enhancement. A dramatic shift in the coupled plasmon resonance is observed as the gap size is varied from 0.39 to 0.41 nm. Existing theoretical models are unable to account for the observed spectral tuning, which requires inclusion of the quantum-classical interface, emphasizing the need for new treatments of light at the subnanoscale.