The addition of a 28 m Cherenkov telescope (CT5) to the H.E.S.S. array extended the experiment's sensitivity to lower energies, providing new opportunities for studies of Active Galactic Nuclei (AGNs) with soft intrinsic spectra and at high redshifts. The high-frequency peaked BL Lac objects PKS 2155-304 (z = 0.116) and PG 1553+113 (0.43 < z < 0.58) are among the brightest objects in the gamma-ray sky, both showing clear signatures of gamma-ray absorption at E > 100 GeV interpreted as being due to interactions with the extragalactic background light (EBL). Multiple observational campaigns of PKS 2155-304 and PG 1553+113 were conducted during 2013 using the full H.E.S.S. II array (CT1-5). To achieve the lowest energy threshold, a monoscopic analysis of the data taken with CT5 was developed along with an investigation into the systematic uncertainties on the spectral parameters which are derived from this analysis. The energy spectra were reconstructed down to energies of 80 GeV for PKS 2155-304, which transits near zenith, and 110 GeV for the more northern PG 1553+113. The measured spectra, well fitted in both cases by a log-parabola spectral model (with a 5 sigma statistical preference for non-zero curvature for PKS 2155-304 and 4.5 sigma for PG 1553+113), were found consistent with spectra derived from contemporaneous Fermi-LAT data, indicating a sharp break in the observed spectra of both sources at E ~ 100 GeV. When corrected for EBL absorption, the intrinsic spectrum of PKS 2155-304 was found to show significant curvature. For PG 1553+113, however, no significant detection of curvature in the intrinsic spectrum could be found within statistical and systematic uncertainties.