Residential consumers have become active participants in the power distribution network after being equipped with residential EV charging provisions. This creates a challenge for the network operator tasked with dispatching electric power to the residential consumers through the existing distribution network infrastructure in a reliable manner. In this paper, we address the problem of scheduling residential EV charging for multiple consumers while maintaining network reliability. An additional challenge is the restricted exchange of information: where the consumers do not have access to network information and the network operator does not have access to consumer load parameters. We propose a distributed framework which generates an optimal EV charging schedule for individual residential consumers based on their preferences and iteratively updates it until the network reliability constraints set by the operator are satisfied. We validate the proposed approach for different EV adoption levels in a synthetically created digital twin of an actual power distribution network. The results demonstrate that the new approach can achieve a higher level of network reliability compared to the case where residential consumers charge EVs based solely on their individual preferences, thus providing a solution for the existing grid to keep up with increased adoption rates without significant investments in increasing grid capacity.