Current postprocessing techniques often require separate models for each lead time and disregard possible inter-ensemble relationships by either correcting each member separately or by employing distributional approaches. In this work, we tackle these shortcomings with an innovative, fast and accurate Transformer which postprocesses each ensemble member individually while allowing information exchange across variables, spatial dimensions and lead times by means of multi-headed self-attention. Weather forecasts are postprocessed over 20 lead times simultaneously while including up to fifteen meteorological predictors. We use the EUPPBench dataset for training which contains ensemble predictions from the European Center for Medium-range Weather Forecasts' integrated forecasting system alongside corresponding observations. The work presented here is the first to postprocess the ten and one hundred-meter wind speed forecasts within this benchmark dataset, while also correcting two-meter temperature. Our approach significantly improves the original forecasts, as measured by the CRPS, with 16.5\% for two-meter temperature, 10\% for ten-meter wind speed and 9\% for one hundred-meter wind speed, outperforming a classical member-by-member approach employed as a competitive benchmark. Furthermore, being up to six times faster, it fulfills the demand for rapid operational weather forecasts in various downstream applications, including renewable energy forecasting.