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 (\(R_{eff} \propto \nu^{0.34 \pm 0.08}\)). 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 is observed. Moreover, it comes closest to matching the data only on timescales much shorter (\(\le 1\) Myr) than the putative UZ Tau age (~2-3 Myr). These discrepancies are the 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 (\(r \lesssim20\) au), they can also explain the observed spatial gradient in the UZ Tau E disk spectrum.