  We present LAMOST J0140355+392651 (hereafter J0140), a close ($P_{\rm orb} =
3.81$ hours) binary containing a bloated, low-mass ($M \approx 0.15 M_{\odot}$)
proto-white dwarf (WD) and a massive ($M\approx 0.95\,M_{\odot}$) WD companion.
The system's optical light curve is dominated by large-amplitude ellipsoidal
variability but also exhibits additional scatter, likely driven by pulsations.
The proto-WD is cooler ($T_{\rm eff} = 6800\pm 100$ K) and more puffy
($\log\left[g/\left({\rm cm\,s^{-2}}\right)\right]=4.74\pm0.07$) than any known
extremely low mass (ELM) WD, but hotter than any known cataclysmic variable
(CV) donor. It either completely or very nearly fills its Roche lobe
($R/R_{{\rm Roche\,lobe}}=0.99\pm0.01$), suggesting ongoing or recently
terminated mass transfer. No dwarf nova-like outbursts have been observed. The
spectrum is dominated by the proto-WD but shows tentative hints of H$\alpha$
emission, perhaps due to accretion onto the massive WD. The properties of the
system are well-matched by MESA binary evolution models of CVs with donors that
underwent significant nuclear evolution before the onset of mass transfer. In
these models, the bloated proto-WD is either still losing mass via stable Roche
lobe overflow or was doing so until very recently. In either case, it is
evolving toward higher temperatures at near-constant luminosity to become an
ELM WD. If the system is detached, mass transfer likely ended when the donor
became too hot for magnetic braking to remain efficient. Evolutionary models
predict that the binary will shrink to $P_{\rm orb}\lesssim 10$ minutes within
a few Gyr, when it will either merge or become an AM CVn binary. J0140 provides
an observational link between the formation channels of CVs, ELM WDs, detached
ultracompact WD binaries, and AM CVn systems.
