This paper proposes a novel hierarchical energy market design modeling the interactions between a distribution system operator (DSO) and a community of smart prosumers equipped with renewable energy generation and energy storage devices. The DSO sets dynamic energy prices to optimize its revenue, whereas prosumers strategize their energy procurement and the operational schedules of their storage devices to minimize costs. We formalize the problem of designing optimal dynamic energy prices as a large-scale Stackelberg game and deploy BIG Hype, a novel first-order algorithm, to obtain a locally optimal solution. Finally, we show via numerical simulations that the increased flexibility of our market design yields substantial economic advantages to the DSO, and that the proposed solution approach is effective even in scenarios involving a large prosumers base.