The molecular structure of electric double layers (EDLs) at electrode-electrolyte interfaces is crucial for all types of electrochemical processes. Here, we probe the EDL structure of an ionic liquid, 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide (BMPy-TFSI), using electrochemical shell-isolated nanoparticle-enhanced Raman spectroscopy. We extract the position and intensity of individual peaks corresponding to either intra- or inter-molecular vibrational modes and examine their dependence on the electrode potential. The observed trends suggest that the molecular reconfiguration mechanism is distinct between cations and anions. BMPy+ is found to always adsorb on the Au electrode surface via the pyrrolidinium ring while the alkyl chains strongly change their orientation at different potentials. In contrast, TFSI- is observed to have pronounced position shifts but negligible orientation changes as we sweep the electrode potential. Despite their distinct reconfiguration mechanisms, BMPy+ and TFSI- in the EDL are likely paired together through strong intermolecular interaction.