Recent observations from JWST have revealed an abundance of Seyfert-luminosity AGN at high redshift that lack any observable X-ray counterparts. Current theories provide two reasons for such X-ray deficits: (1) rapid accretion with very soft X-ray spectra akin to Narrow Line Seyfert 1s in the local universe or (2) AGN obscured by Compton-thick levels of obscuration along the line-of-sight. However, no example is currently known of an AGN displaying both a soft spectrum and Compton-thick obscuration at any redshift. In this talk, I will present the first and currently only NuSTAR confirmed Compton-thick AGN with strong indications of an intrinsically soft X-ray spectrum, existing at a mere 22 Mpc from us. By testing multiple model geometries for the obscurer, we show that the observed X-ray spectrum can only be explained with either (i) an extraordinarily steep slope with photon index of ~3, (ii) a remarkably low coronal temperature of <~ 15 keV or (iii) a combination of both. All three possibilities suggest the source is the first Narrow Line Seyfert 1 confirmed to be obscured by Compton-thick obscuration along the line-of-sight. However, regardless of its accretion properties, intrinsically X-ray soft Compton-thick AGN plausibly represent an entirely new class of obscured AGN that would be essentially invisible to all wide-area X-ray surveys performed to-date. Such sources thus provide a natural explanation for JWST AGN lacking detectable X-ray counterparts at high redshift.