The evolution of young stars and disks is driven by the interplay of several processes, notably the accretion and ejection of material. These processes, critical to correctly describe the conditions of planet formation, are best probed spectroscopically. Between 2020 and 2022, about 500orbits of the Hubble Space Telescope (HST) are being devoted in to the ULLYSES public survey of about 70 low-mass (M⋆ ≤ 2 M⊙) young (age < 10 Myr) stars at UV wavelengths. Here, we present the PENELLOPE Large Program carried out with the ESO Very Large Telescope (VLT) with the aim of acquiring, contemporaneously to the HST, optical ESPRESSO/UVES high-resolution spectra for the purpose of investigating the kinematics of the emitting gas, along with UV-to-NIR X-shooter medium-resolution flux-calibrated spectra to provide the fundamental parameters that HST data alone cannot provide, such as extinction and stellar properties. The data obtained by PENELLOPE have no proprietary time and the fully reduced spectra are being made available to the whole community. Here, we describe the data and the first scientific analysis of the accretion properties for the sample of 13 targets located in the Orion OB1 association and in the σ-Orionis cluster, observed in November-December 2020. We find that the accretion rates are in line with those observed previously in similarly young star-forming regions, with a variability on a timescale of days (≲3). The comparison of the fits to the continuum excess emission obtained with a slab model on the X-shooter spectra and the HST/STIS spectra shows a shortcoming in the X-shooter estimates of ≲10%, which is well within the assumed uncertainty. Its origin can be either due to an erroneous UV extinction curve or to the simplicity of the modeling and, thus, this question will form the basis of the investigation undertaken over the course of the PENELLOPE program. The combined ULLYSES and PENELLOPE data will be key in attaining a better understanding of the accretion and ejection mechanisms in young stars.