About 70 percent of stars in the Milky Way galaxy are M-dwarfs. They span a range of low masses (0.08 - 0.6 solar mass), have faint luminosities (less than 0.05 solar luminosity), and temperatures ranging between 2500 K - 4000 K, facilitating molecule formation throughout their atmospheres. Standard stellar analysis methods to accurately characterize them have thus far proved challenging—in not correctly accounting for vast variations in their atmospheric structures. Our modeling framework will determine fundamental atmospheric properties of M-dwarfs with a two-pronged approach: a physically motivated self-consistent radiative-convective model grid with up-to-date opacities, constrained by thermo-chemical and hydrostatic equilibrium, radiative and convective transport as well as a data-driven Bayesian retrieval technique. We leverage the broadband molecular absorption features occurring in low-resolution M-dwarf spectra (from SpeX Prism Library) and use them to our advantage in acquiring robust constraints on the effective temperature, surface gravity and bulk chemical properties of M-dwarf atmospheres. Our approach lies in the interface between the standard self-consistent prescription for modeling stellar atmospheres and an assumption-free data-driven retrieval method, where new physical intuition can be obtained about our understanding of low-mass stars.