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This paper seeks to address the profound power resilience inequity in New York City by means of strategic allocation of electric vehicle (EV) charging infrastructure to support the power grid operation in challenging scenarios, such as when facing high demand or during natural disasters. First, we uncover the most disproportionately affected communities in New York by developing a metric of power resilience inequity to measure the combined impact of power failure-related factors on these areas. We employ data-driven approaches to infer the statistical relationships between communities' power resilience index, their available EV charging infrastructure, and several other prominent socio-demographical variables. This inference yields the development of a machine learning model that can predict the reduction of power resilience inequity after deployment of the proposed resource allocation strategy. We further develop an optimization framework that jointly considers equity and efficiency to guide the optimized distribution of EV charging infrastructure across the city. A number of case studies are leveraged to demonstrate the capability of the devised approach in enhancing urban power resilience equity, yielding favorable results in marginalized communities. [ABSTRACT FROM AUTHOR]