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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$, [\ion{O}{II}]$λ\lambda3727,3729$ , [\ion{Ne}{III}]$\lambda3869$, H$γ$, [\ion{O}{III}]$\lambda4363$, H$β$, [\ion{O}{III}]$\lambda4959$, [\ion{O}{III}]$\lambda5007$, and H$α$. 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.