Under-display cameras have been proposed in recent years as a way to reduce the form factor of mobile devices while maximizing the screen area. Unfortunately, placing the camera behind the screen results in significant image distortions, including loss of contrast, blur, noise, color shift, scattering artifacts, and reduced light sensitivity. In this paper, we propose an image-restoration pipeline that is ISP-agnostic, i.e. it can be combined with any legacy ISP to produce a final image that matches the appearance of regular cameras using the same ISP. This is achieved with a deep learning approach that performs a RAW-to-RAW image restoration. To obtain large quantities of real under-display camera training data with sufficient contrast and scene diversity, we furthermore develop a data capture method utilizing an HDR monitor, as well as a data augmentation method to generate suitable HDR content. The monitor data is supplemented with real-world data that has less scene diversity but allows us to achieve fine detail recovery without being limited by the monitor resolution. Together, this approach successfully restores color and contrast as well as image detail.