At a distance of only 1.3 pc, Proxima Cen is the closest exoplanetary system orbiting an M-type flare star, making it a benchmark case to explore the properties and potential effects of stellar activity on exoplanet atmospheres. Our previous discovery of a flare from Proxima Cen at millimeter wavelengths with the Atacama Large Millimeter/submillimeter Array (ALMA) has opened up an entirely new observational regime to study stellar flaring mechanisms. These are the first results from a larger campaign consisting of roughly 40 hours of simultaneous observations spanning radio to X-ray wavelengths. Here, we present the discovery of a second flaring event on 1 May 2019 from Proxima Cen with ALMA, but this time complemented by multi-wavelength observations with the Hubble Space Telescope (HST) of far-ultraviolet (FUV) spectroscopy, the Transiting Exoplanet Survey Satellite (TESS) of optical photometry, and the DuPont telescope at Las Campanas of optical spectroscopy. In the millimeter and FUV, the May 1 flare is the brightest ever detected from Proxima Cen, brightening by a factor of >1000 and >14000 as seen by ALMA and HST, respectively. The millimeter and FUV continuum emission trace each other very closely during the flare, exhibiting similar rise and decay times, peaking near simultaneously, and achieving large enhancements in luminosity. Optical emission is somewhat decoupled, peaking at a much lower level with a slight time delay. Given the unique characteristics of this event, it is possible that we are seeing an entirely new type of flare. The extremely short duration of this event suggests that it could originate from a single flare loop or 'building block’ instead of an arcade structure consisting of multiple superimposed loops. The strong correlation between millimeter and FUV emission allows us to determine a tentative scaling relation. If this holds for a larger sample of events, millimeter emission could serve as a proxy for FUV emission from stellar flares and become a powerful new tool to constrain the high energy radiation environment of planets orbiting flare stars, required input for models of planetary atmosphere evolution.