Plasma dynamics critically depends on density and temperature, thus well-controlled experimental realizations are essential benchmarks for theoretical models. The formation of an ultracold plasma can be triggered by ionizing a tunable number of atoms in a micrometer-sized volume of a 87Rb Bose-Einstein condensate (BEC) by a single femtosecond laser pulse. The large density combined with the low temperature of the BEC give rise to an initially strongly coupled plasma in a so far unexplored regime bridging ultracold neutral plasma and ionized nanoclusters. Here, we report on ultrafast cooling of electrons, trapped on orbital trajectories in the long-range Coulomb potential of the dense ionic core, with a cooling rate of 400 K/ps. Furthermore, our experimental setup grants direct access to the electron temperature that relaxes from 5250 K to below 10 K in less than 500 ns.