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We have discovered spectacular vast molecular gas reservoirs reaching tens of kpc outside of two high-redshift post-starburst galaxies as part of an ongoing ALMA survey of such objects. While the host galaxies are only 3-5kpc in size comma nearly half the total molecular gas in each system extends 25-45kpc from the hosts. This discovery was unexpected and both the scale and magnitude of the extended gas features are unprecedented at any redshift. The origin of the highly extended molecular gas we have discovered is unclear comma but may be related to AGN outflows comma stripped tidal tails comma and-or material cooled from hotter circumgalactic gas - the spatial resolution and sensitivity of HST are needed to distinguish which. We propose an efficient comma high-impact program using WFC3 G102 slitless spectroscopy and F105W direct imaging to determine the origins of the remarkable gas features and their broader implications for galaxy evolution comma including galactic feedback comma the formation of extended stellar halos comma and circumgalactic metal enrichment. These observations are designed to detect and resolve in-situ star formation within the extended gas features comma identify stellar tidal debris and close-in merging companions comma and spectroscopically map out the local environment on 1Mpc scales. Together comma the combination of direct imaging and slitless spectroscopy can uniquely determine the origin of the incredible molecular gas structures we have found and place this unexpected discovery in broader context.