There is a large body of historical documents that are too fragile to be opened or unrolled, making their contents inaccessible. Recent improvements in X-ray scanning technology and computer vision techniques make it possible to perform a "virtual" unrolling of such documents. We describe a novel technique to process a stack of 3D X-ray images to identify the surface of parchment scrolls, unroll them, and create a visualization of their written contents. Unlike existing techniques, we can handle even challenging cases with minimal manual interaction. Our novel approach was deployed on two 15th and 16th century damaged historic scrolls from the manors of Bressingham and Diss Heywood. The former has become fused, probably due to exposure to moisture, and cannot be fully unrolled. The latter was severely burnt several hundred years ago, becoming thoroughly charred, heat-shrunken, and distorted, with all the sheets now brittle and fused together. Our virtual unrolling revealed text that has been hidden for centuries.