We explore the possibility to systematically study the extended , hot gaseous halos of low-redshift galaxies with Coronal Broad Ly \alpha Absorbers ( CBLAs ) . These are weak , thermally broadenend H i absorption lines arising from the tiny fraction of neutral hydrogen that resides in the collisionally ionized , million-degree halo gas in these galaxies . Using a semi-analytic approach , we model the spatial density and temperature distribution of hot coronal gas to predict strength , spectral shape , and cross section of CBLAs as a function of galaxy-halo mass and line-of-sight impact parameter . For virial halo masses in the range log ( M / M _ { \sun } ) = 10.6 - 12.6 , the characteristic logarithmic CBLA H i column densities and Doppler parameters are log N ( H i ) = 12.4 - 13.4 and b ( H i ) = 70 - 200 km s ^ { -1 } , indicating that CBLAs represent weak , shallow spectral features that are difficult to detect . Yet , the expected number density of CBLAs per unit redshift in the above given mass range is d { \cal N } / dz ( CBLA ) \approx 3 , implying that CBLAs have a substantial absorption cross-section . We compare the model predictions with a combined set of ultraviolet ( UV ) absorption-line spectra from HST/COS and HST/STIS that trace the halos of four low-redshift galaxies . We demonstrate that CBLAs already might have been detected in these spectra , but the complex multi-component structure and the limited signal-to-noise ratio ( S/N ) complicate the interpretation of these CBLA candidate systems . Our study suggests that CBLAs represent a very interesting absorber class that potentially will allow us to further explore the hot coronae of galaxies with UV spectral data .