Brightness is a key figure of merit for charged particle beams, and time-resolved brightness measurements can elucidate the processes involved in beam creation and manipulation. Here we report on a simple, robust, and widely applicable method for the measurement of beam brightness with temporal resolution by streaking one-dimensional pepperpots, and demonstrate the technique to characterize electron bunches produced from a cold-atom electron source. We demonstrate brightness measurements with 145 ps temporal resolution and a minimum resolvable emittance of 40 nm rad. This technique provides an efficient method of exploring source parameters and will prove useful for examining the efficacy of techniques to counter space-charge expansion, a critical hurdle to achieving single-shot imaging of atomic scale targets.