  High-resolution spectrographs open a detailed window onto the atmospheres of
stars and planets. As the number of systems observed with different instruments
grows, it is crucial to develop a standard in analyzing spectral time series of
exoplanet transits and occultations, for the benefit of reproducibility. Here,
we introduce the ANTARESS workflow, a set of methods aimed at processing
high-resolution spectroscopy datasets in a robust way and extracting accurate
exoplanetary and stellar spectra. While a fast preliminary analysis can be run
on order-merged 1D spectra and cross-correlation functions (CCFs), the workflow
was optimally designed for extracted 2D echelle spectra to remain close to the
original detector counts, limit the spectral resampling, and propagate the
correlated noise. Input data from multiple instruments and epochs were
corrected for relevant environmental and instrumental effects, processed
homogeneously, and analyzed independently or jointly. In this first paper, we
show how planet-occulted stellar spectra extracted along the transit chord and
cleaned from planetary contamination provide a direct comparison with
theoretical stellar models and enable a spectral and spatial mapping of the
photosphere. We illustrate this application of the workflow to archival
ESPRESSO data, using the Rossiter-McLaughlin effect Revolutions (RMR) technique
to confirm the spin-orbit alignment of HD\,209458b and unveil biases in
WASP-76b's published orbital architecture. Because the workflow is modular and
its concepts are general, it can support new methods and be extended to
additional spectrographs to find a range of applications beyond the proposed
scope. In a companion paper, we will present how planet-occulted spectra can be
processed further to extract and analyze planetary spectra decontaminated from
the star, providing clean and direct measurements of atmospheric properties.
