Short-period white-dwarf--main-sequence (WDMS) binaries provide direct constraints on the outcomes of common-envelope (CE) evolution and the survival of low-mass companions during engulfment. We report the discovery and confirmation of 10 totally eclipsing WD + cool-M-dwarf binaries identified through a search tailored to minute-scale eclipses in Transiting Exoplanet Survey Satellite (TESS) high-cadence data and validated with SPECULOOS multiband photometry. The systems have orbital periods of a few hours and companion masses of 0.094--0.175 M⊙. Our pilot search of ~37,000 Gaia-selected WDs increases the number of WD+M systems first identified through TESS by an order of magnitude, demonstrating that minute-scale WD eclipses occupy a previously underexplored discovery regime for TESS. SPECULOOS follow-up establishes the WDs as the sources of the eclipse signals, while chromatic eclipse dilution and broadband spectral-energy-distribution (SED) modeling provide complementary constraints on the component properties. These systems extend the TESS-discovered eclipsing WD+M population toward lower companion masses and establish an effective, scalable framework for expanding the search from the ~37,000 WDs analyzed here to a pool of O(106) Gaia WD candidates with TESS photometry.