Mass adoption of the plug-in electric vehicle (EV) technology is imperative for the rapid electrification of the transportation sector to mitigate catastrophic effects from climate change. Rapid integration of a large number of EVs will inevitably cause uncertainty and variability on the operation of the existing electric power system. There is high uncertainty on not only the speed and scale of EV adoption but also the EV energy and power requirements that depends on EV charging patterns. This study uses energy meter-level data from the San Diego region to analyze the energy load profiles of residential customers under the time-of-use (TOU) rate with and without EV charging requirements. Unlike previous forecasts on the effects of EV charging loads, the energy load profile of TOU customers with EVs reveal a "twin demand peak" where there is a peak demand during the evening hours and another at midnight. Results reveal potential issues for grid operations with greater EV adoption and the importance of careful TOU rate design.