Abstract Comparison of échelle spectra to synthetic models has become a computational statistics challenge, with over 10,000 individual spectral lines affecting a typical cool star échelle spectrum. Telluric artifacts, imperfect line lists, inexact continuum placement, and inflexible models frustrate the scientific promise of these information-rich data sets. Here we debut an interpretable machine-learning framework blasé that addresses these and other challenges. The semiempirical approach can be viewed as “transfer learning”—first pretraining models on noise-free precomputed synthetic spectral models, then learning the corrections to line depths and widths from whole-spectrum fitting to an observed spectrum. The auto-differentiable model employs back-propagation, the fundamental algorithm empowering modern deep learning and neural networks. Here, however, the 40,000+ parameters symbolize physically interpretable line profile properties such as amplitude, width, location, and shape, plus radial velocity and rotational broadening. This hybrid data-/model-driven framework allows joint modeling of stellar and telluric lines simultaneously, a potentially transformative step forward for mitigating the deleterious telluric contamination in the near-infrared. The blasé approach acts as both a deconvolution tool and semiempirical model. The general-purpose scaffolding may be extensible to many scientific applications, including precision radial velocities, Doppler imaging, chemical abundances for Galactic archeology, line veiling, magnetic fields, and remote sensing. Its sparse-matrix architecture and GPU acceleration make blasé fast. The open-source PyTorch-based code blase includes tutorials, Application Programming Interface documentation, and more. We show how the tool fits into the existing Python spectroscopy ecosystem, demonstrate a range of astrophysical applications, and discuss limitations and future extensions.