We perform microwave imaging using a dynamically reconfigurable aperture based on a tunable, disordered cavity. The electrically-large cavity is cubic, with a spherical-deformation, and supports a multitude of distinct electromagnetic modes that vary as a function of excitation frequency. With a set of irises introduced into one wall of the cavity, the cavity modes couple to spatially-distinct radiative modes that vary as a function of the driving frequency. To increase the diversity of the radiated fields, we replace one of the cavity walls with a variable impedance surface consisting of a set of varactor-populated mushroom structures grouped into pixels. The reflection phase of each pixel is independently changed with application of a voltage bias, effectively altering the surface impedance. We demonstrate high-fidelity imaging and examine the role of the impedance-tunable boundary condition, revealing superior performance in comparison with just frequency-diverse measurements. We also demonstrate single-frequency imaging, which could significantly reduce the demands on the required microwave source. The dynamic cavity imager may find relevance in security screening, through-wall imaging, biomedical diagnostics, and radar applications.