Large-scale transport electrification requires economically viable EV charging infrastructure with limited impact on distribution networks, especially under electricity price volatility. This paper presents a techno-economic planning and operation model for a grid-connected EV-charging microgrid integrating photovoltaic and wind generation together with battery energy storage. The proposed techno-economic model is formulated as a linear program that co-optimizes component capacities and hourly dispatch over a multi-year horizon by minimizing the levelized cost of energy (LCOE) while considering technical constraints related to power balance and energy component operation limitations. The case study considers two scenarios related to EV charging power supply: base scenario and renewable-only EV charging scenario to quantify the trade-off between costs and sustainability.