The present study confirms BD-14\,3065b as a transiting planet-brown dwarf in a triple-star system, with a mass near the deuterium-burning boundary. BD-14\,3065b has the largest radius observed within the sample of giant planets and brown dwarfs around post-main sequence stars. Its orbital period is 4.3 days and it transits a subgiant F-type star with a mass of $M_ odot $, a radius of $R_ odot $, an effective temperature of $T_ eff and a metallicity of $-0.34 By combining TESS photometry with high-resolution spectra acquired with the TRES and Pucheros+ spectrographs, we measured a mass of $M_p=12.37 and a radius of $R_p=1.926 Our discussion of potential processes that could be responsible for the inflated radius led us to conclude that deuterium burning is a plausible explanation for the heating taking place in BD-14\,3065b's interior. Detections of the secondary eclipse with TESS photometry enabled a precise determination of the eccentricity, $e_p=0.066 and reveal that BD-14\,3065b has a brightness temperature of $3520 130$\,K. With its unique characteristics, BD-14\,3065b presents an excellent opportunity to study its atmosphere via thermal emission spectroscopy.