A unique feature of the LOFAR radio telescope, we developed, is the ability to catch ultra-short radio flashes with its new transient buffer boards. Ultra-short radio flashes represent a largely uncharted territory and can have widely different origins: from cosmic particles hitting our atmosphere to radio emission produced by neutron stars collapsing to a black hole. Here, we use this technique to investigate two of the most fascinating questions in high-energy astrophysics: the nature of cosmic rays and the origin of fast radio bursts. Cosmic rays are particles accelerated in cosmic sources to energies far exceeding anything achievable in particle accelerators, such as the LHC. Nature and origin of high-energy cosmic rays are still unknown. Using LOFAR we can now measure and decode radio flashes from cosmic rays, hitting the earth atmosphere in great detail, tentatively revealing a mix of Galactic iron and extragalactic hydrogen nuclei at 1017-1018 eV. Improving our measurements by an order of magnitude, we want to do the first high-precision composition measurement of cosmic rays in this energy range and clarify where cosmic rays are accelerated and what they are made of. Moreover, fast radio bursts have recently been discovered by high-frequency radio telescopes, which pose a complete mystery. The bursts might be due to cataclysmic explosions in the early universe, stars in our Milky Way, or something even closer to home. By adapting our cosmic-ray mode, fast radio bursts could be caught in the act, thereby allowing LOFAR to solve the riddle of their origin.