We consider an energy harvesting transmitter broadcasting individual data to two receivers. Data packets intended for each user are assumed to arrive at arbitrary but known instants. The goal is to minimize the total transmission time of the packets arriving within a certain time window, using the energy harvested during this time. Energy harvests are also modelled to occur at known discrete instants. An achievable rate region with structural properties satisfied by the two-user additive white Gaussian noise broadcast channel capacity region is assumed. Structural properties of power and rate allocations are established, as well as the uniqueness of the optimal policy. An iterative algorithm, DuOpt, is devised for efficient solution of this offline problem. DuOpt is compared with the sequential unconstrained minimization (SUMT) solution technique on randomly generated problem instances and is observed to solve the problem two orders of magnitude faster on average than SUMT.