Ion correlations have been suggested as the underlying mechanism of a number of counterintuitive phenomena in soft condensed-matter, such as like-charge attraction. Recently, several theoretical models have emerged, attempting to address these electrostatic correlations, beyond the mean field description of the Poisson-Boltzmann theory. The central prediction of these theories, the ion density profile, has remained untested by measurements with microscopic resolution. In this work, we present the first molecular-level tests of an ion correlations model. Analysis of synchrotron x-ray reflectivity using a phenomenological model reveals ion condensation at the liquid/liquid interface, when polarized with an electric field. Tuning the density of this ionic layer allows for a detailed study of ion correlations as a function of the Coulomb coupling strength in the system. We propose a density functional theory that aims to describe electrostatic ion correlations and explicitly includes solvent effects through an ion-solvent interaction potential, mapped out using Molecular Dynamics simulations. The proposed model predicts global electrostatic properties of the system that are in excellent agreement with thermodynamic measurements of the interfacial excess charge, with no adjustable parameters. Comparison of the density profiles to the x-ray data indicates that a nonlocal free functional based on the Debye-Huckel-Hole theory of a one-component plasma, adequately describes ion-ion interactions up to a correlation strength of 4 k_B T. We anticipate this result to be of relevance in other strongly correlated soft matter systems.