Uncertainty quantification (UQ) methods play an important role in reducing errors in weather forecasting. Conventional approaches in UQ for weather forecasting rely on generating an ensemble of forecasts from physics-based simulations to estimate the uncertainty. However, it is computationally expensive to generate many forecasts to predict real-time extreme weather events. Evidential Deep Learning (EDL) is an uncertainty-aware deep learning approach designed to provide confidence about its predictions using only one forecast. It treats learning as an evidence acquisition process where more evidence is interpreted as increased predictive confidence. We apply EDL to storm forecasting using real-world weather datasets and compare its performance with traditional methods. Our findings indicate that EDL not only reduces computational overhead but also enhances predictive uncertainty. This method opens up novel opportunities in research areas such as climate risk assessment, where quantifying the uncertainty about future climate is crucial.