The topic of high dynamic range (HDR) tomography is starting to gain attention due to recent advances in the hardware technology. Registering high-intensity projections that exceed the dynamic range of the detector cause sensor saturation. Existing methods rely on the fusion of multiple exposures. In contrast, we propose a one-shot solution based on the Modulo Radon Transform (MRT). By exploiting the modulo non-linearity, the MRT encodes folded Radon Transform projections so that the resulting measurements do not saturate. Our recovery strategy is pivoted around a property we call compactly λ-supported, which is motivated by practice; in many applications the object to be recovered is of finite extent and the measured quantity has approximately compact support. Our theoretical results are illustrated by numerical simulations with an open-access X-ray tomographic dataset and lead to substantial improvement in the HDR recovery problem. For instance, we report recovery of objects with projections 1000x larger in amplitude than the detector threshold.