We present high spatial resolution observations of the continuum emission from the young multiple star system UZ Tau at frequencies from 6 to 340 GHz. To quantify the spatial variation of dust emission in the UZ Tau E circumbinary disk, the observed interferometric visibilities are modeled with a simple parametric prescription for the radial surface brightnesses at each frequency. We find evidence that the spectrum steepens with radius in the disk, manifested as a positive correlation between the observing frequency and the radius that encircles a fixed fraction of the emission (Reff ∝ 0.34 0.08). The origins of this size-frequency relation are explored in the context of a theoretical framework for the growth and migration of disk solids. While that framework can reproduce a similar size-frequency relation, it predicts a steeper spectrum than that observed. Moreover, it comes closest to matching the data only on timescales much shorter (≤1 Myr) than the putative UZ Tau age (∼2-3 Myr). These discrepancies are direct consequences of the rapid radial drift rates predicted by models of dust evolution in a smooth gas disk. One way to mitigate that efficiency problem is to invoke small-scale gas pressure modulations that locally concentrate drifting solids. If such particle traps reach high-continuum optical depths at 30-340 GHz with a ∼30%-60% filling fraction in the inner disk (r 20 au), they can also explain the observed spatial gradient in the UZ Tau E disk spectrum.