We present the first high resolution (0.046" or ~6 au) results on the binary Class I source Oph IRS43 from the Atacama Large Millimeter/submillimeter Array (ALMA) large program, Early Planet Formation in Embedded Disks (eDisk). The 1.3 mm (Band 6) dust continuum observations resolve a small disk, ~6 au radius, around the primary and show that the disk around the secondary is even smaller, <4 au. The line data show that an outflow has cleared a large cavity in a low mass circumbinary envelope that is detected primarily in CO, 13CO, C18O, H2CO, and SO, with kinematic signatures of combined infall and Keplerian rotation extending beyond ~1500 au in radius. There are also faint detections of the organics DCN, c-C3H2, CH3OH. An expanding CO bubble centered on the extrapolated location of the source ~130 years ago suggests a recent ejection event. Despite the small size of the disks, the overall picture is of a remarkably large and dynamically active region. Amongst the eDisk sample, IRS43 is the binary with the closest separation and smallest resolved disk. Given that many stars are born with companions, characterizing early-stage protobinary disks is crucial to understand how multiplicity can affect the resulting properties of both the stars and the potential planetary systems.