Massive star-forming regions exhibit an extremely rich and diverse chemistry, which in principle provides a wealth of molecular probes, as well as laboratories for interstellar prebiotic chemistry. Since the chemical structure of these sources displays substantial spatial variation among species on small scales (${lesssim}10^4$ au), high angular resolution observations are needed to connect chemical structures to local environments and inform astrochemical models of massive star formation. To address this, we present ALMA 1.3 mm observations toward OB cluster-forming region G10.6-0.4 (hereafter G10.6) at a resolution of 0.14$^{primeprime}$ (700 au). We find highly-structured emission from complex organic molecules (COMs) throughout the central 20,000 au, including two hot molecular cores and several shells or filaments. We present spatially-resolved rotational temperature and column density maps for a large sample of COMs and warm gas tracers. These maps reveal a range of gas substructure in both O- and N-bearing species. We identify several spatial correlations that can be explained by existing models of COM formation, including NH$_2$CHO/HNCO and CH$_3$OCHO/CH$_3$OCH$_3$, but also observe unexpected distributions and correlations which suggest that our current understanding of COM formation is far from complete. Importantly, complex chemistry is observed throughout G10.6, rather than being confined to hot cores. The COM composition appears to be different in the cores compared to the more extended structures, which illustrates the importance of high spatial resolution observations of molecular gas in elucidating the physical and chemical processes associated with massive star formation.