potential for quantum tomography or spectroscopy is largely unexplored. We develop here a CQED formalism for monitoring the dynamics of a complex quantum system, deriving a set of Stochastic Hierarchy Equations of Motion to describe continuous measurement in presence of non-perturbative and non-Markovian decoherence effects. Using the cavity as a probe enables us to engineer a continuous measurement observable by tuning either the cavity frequency, the cavity drive phase or the detector phase. This turns the cavity into a tool for continuous quantum state tomography with no need for active control. We further demonstrate that time correlations of the detector record can provide a spectroscopic probe of the non-Markovian nature of the decoherence dynamics.