Many atlases used for brain parcellation are hierarchically organised, progressively dividing the brain into smaller sub-regions. However, state-of-the-art parcellation methods tend to ignore this structure and treat labels as if they are `flat'. We introduce a hierarchically-aware brain parcellation method that works by predicting the decisions at each branch in the label tree. We further show how this method can be used to model uncertainty separately for every branch in this label tree. Our method exceeds the performance of flat uncertainty methods, whilst also providing decomposed uncertainty estimates that enable us to obtain self-consistent parcellations and uncertainty maps at any level of the label hierarchy. We demonstrate a simple way these decision-specific uncertainty maps may be used to provided uncertainty-thresholded tissue maps at any level of the label tree.