The European Spallation Source being constructed in Lund, Sweden will provide the user community with a neutron source of unprecedented brightness. By 2025, a suite of 15 instruments will be served by a high-brightness moderator system placed above the spallation target. The ESS infrastructure, consisting of the proton linac, the target station, and the instrument halls, allows for implementation of a second source below the spallation target. We propose to develop a second neutron source with a high-intensity moderator able to (1) deliver a larger total cold neutron flux, (2) provide high intensities at longer wavelengths in the spectral regions of Cold (4–10 Å), Very Cold (10–40 Å), and Ultra Cold (several 100 Å) neutrons, as opposed to Thermal and Cold neutrons delivered by the top moderator. Offering both unprecedented brilliance, flux, and spectral range in a single facility, this upgrade will make ESS the most versatile neutron source in the world and will further strengthen the leadership of Europe in neutron science. The new source will boost several areas of condensed matter research such as imaging and spin-echo, and will provide outstanding opportunities in fundamental physics investigations of the laws of nature at a precision unattainable anywhere else. At the heart of the proposed system is a volumetric liquid deuterium moderator. Based on proven technology, its performance will be optimized in a detailed engineering study. This moderator will be complemented by secondary sources to provide intense beams of Very- and Ultra-Cold Neutrons.