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A fraction of active galactic nuclei (AGN) exhibit dramatic variability, which is observed on timescales down to minutes in the X-ray band. We introduce the case study of 1H 1934-063 (z = 0.0102), a Narrow-line Seyfert 1 (NLS1) among the brightest and most variable AGN ever observed with XMM-Newton. This work includes spectral and temporal analyses of a concurrent XMM-Newton and NuSTAR 2015 observation lasting 130 kiloseconds, during which the X-ray source exhibited a steep (factor of 6) plummet and subsequent full recovery of flux level, accompanied by deviation from a single log-normal flux distribution. We rule out Compton-thin obscuration as the cause for this dramatic variability observed even at NuSTAR energies. In order to constrain coronal geometry, dynamics, and emission/absorption processes, we compare detailed spectral fitting with Fourier-based timing analysis. Similar to other well-studied, highly variable Seyfert 1s, this AGN is X-ray bright and displays strong reflection features. We find a narrower broad iron line component compared to most Seyfert 1s, and constrain black hole spin to be < 0.1, one of the lowest yet discovered for such systems. Combined spectral and timing results are consistent with a dramatic change in the continuum on timescales as short as a few kiloseconds dictating the nature of this variability. We also discover a Fe-K time lag, measuring a delay of 20 seconds between relativistically-blurred reflection off the inner accretion flow and the hard X-ray continuum emission.