  Ionizing photons must have escaped from high-redshift galaxies, but the
neutral high-redshift intergalactic medium makes it unlikely to directly detect
these photons during the Epoch of Reionization. Indirect methods of studying
ionizing photon escape fractions present a way to infer how the first galaxies
may have reionized the universe. Here, we use HET/LRS2 observations of
J0919+4906, a confirmed z$\approx$0.4 emitter of ionizing photons to achieve
spatially resolved (12.5 kpc in diameter) spectroscopy of
\ion{Mg}{II}$\lambda2796$, \ion{Mg}{II}$\lambda2803$,
[\ion{O}{II}]$\lambda\lambda3727,3729$ , [\ion{Ne}{III}]$\lambda3869$,
H$\gamma$, [\ion{O}{III}]$\lambda4363$, H$\beta$, [\ion{O}{III}]$\lambda4959$,
[\ion{O}{III}]$\lambda5007$, and H$\alpha$. From these data we measure
\ion{Mg}{II} emission, which is a promising indirect tracer of ionizing
photons, along with nebular ionization and dust attenuation in multiple
spatially-resolved apertures. We find that J0919+4906 has significant spatial
variation in its \ion{Mg}{II} escape and thus ionizing photon escape fraction.
Combining our observations with photoionization models, we find that the
regions with the largest relative \ion{Mg}{II} emission and \ion{Mg}{II} escape
fractions have the highest ionization and lowest dust attenuation. Some regions
have an escape fraction that matches that required by models to reionize the
early universe, while other regions do not. We observe a factor of 36 spatial
variation in the inferred LyC escape fraction, which is similar to recently
observed statistical samples of indirect tracers of ionizing photon escape
fractions. These observations suggest that spatial variations in neutral gas
properties lead to large variations in the measured LyC escape fractions. Our
results suggest that single sightline observations may not trace the
volume-averaged escape fraction of ionizing photons.
