With advances in nanofabrication techniques, extreme-scale nanophotonic devices with critical gap dimensions of just 1-2 nm have been realized. Plasmons in such ultranarrow gaps can exhibit nonlocal response, which was previously shown to limit the field enhancement and cause optical properties to deviate from the local description. Using atomic layer lithography, we create mid-infrared-resonant coaxial apertures with gap sizes as small as 1 nm and observe strong evidence of nonlocality, including spectral shifts and boosted transmittance of the cutoff epsilon-near-zero mode. Experiments are supported by full-wave 3-D nonlocal simulations performed with the hybridizable discontinuous Galerkin method. This numerical method captures atomic-scale variations of the electromagnetic fields while efficiently handling extreme-scale size mismatch. Combining atomic-layer-based fabrication techniques with fast and accurate numerical simulations provides practical routes to design and fabricate highly-efficient large-area mid-infrared sensors, antennas, and metasurfaces.