We propose the task of Panoptic Scene Completion (PSC) which extends the recently popular Semantic Scene Completion (SSC) task with instance-level information to produce a richer understanding of the 3D scene. Our PSC proposal utilizes a hybrid mask-based technique on the nonempty voxels from sparse multi-scale completions. Whereas the SSC literature overlooks uncertainty which is critical for robotics applications, we instead propose an efficient ensembling to estimate both voxel-wise and instance-wise uncertainties along PSC. This is achieved by building on a multi-input multi-output (MIMO) strategy, while improving performance and yielding better uncertainty for little additional compute. Additionally, we introduce a technique to aggregate permutation-invariant mask predictions. Our experiments demonstrate that our method surpasses all baselines in both Panoptic Scene Completion and uncertainty estimation on three large-scale autonomous driving datasets. Our code and data are available at https://astra-vision.github.io/PaSCo .