Energy-resolving photon-counting CT promises improved material-separation capabilities compared to conventional CT. However, accurate separation of iodine and calcium, which is especially important for imaging atherosclerotic plaques, remains a challenge. In this proof-of-concept study, we present a deep-learning based method that takes a pair of basis images from a photon-counting CT as input and produces a map of the iodine distribution where the contamination from other materials such as calcium is minimized, and demonstrate its performance on clinical images of the carotid arteries. As training data, we used 13 pairs of image slices of the neck from a silicon-based photon-counting spectral CT, with one non-contrast and one contrast-enhanced slice in each pair. To generate a ground-truth iodine maps as training labels, 40 keV virtual monoenergetic non-contrast images were registered to align with the corresponding 40 keV contrast-enhanced images, and the difference between those two image slices was used to generate an iodine concentration map. We trained a ResUNet++ deep convolutional neural network using water-iodine basis image pairs resulting from a two-basis material decomposition as inputs and the iodine concentration map obtained from subtraction as label. The resulting method was evaluated on a previously unseen photon-counting CT image slice of the neck from the same patient. Our results show that the trained network correctly highlights the image features containing iodinated contrast agent and quantifies the concentration accurately. The contamination from calcium and other tissues is significantly reduced compared to the original iodine basis image. Our results demonstrate that the proposed method can successfully separate iodine from calcium and other tissues on clinical silicon-based photon-counting CT, with important potential implications for imaging of atherosclerosis.