The deviation between chronological age and age predicted from neuroimaging data has been identified as a sensitive risk marker of cross-disorder brain changes, growing into a cornerstone of biological age research. However, machine learning models underlying the field do not consider uncertainty, thereby confounding results with training data density and variability. Also, existing models are commonly based on homogeneous training sets, often not independently validated, and cannot be shared because of data protection issues. Here, we introduce an uncertainty-aware, shareable, and transparent Monte Carlo dropout composite quantile regression (MCCQR) Neural Network trained on N = 10,691 datasets from the German National Cohort. The MCCQR model provides robust, distribution-free uncertainty quantification in high-dimensional neuroimaging data, achieving lower error rates compared with existing models. In two examples, we demonstrate that it prevents spurious associations and increases power to detect deviant brain aging. We make the pretrained model and code publicly available.