The B+-tree is a ubiquitous search index due to its provable I/O (cache) efficiency. Yet unlike batch-parallel binary search trees, which are both fast and widely available, no batch-parallel B+-tree offers strong empirical performance together with provable, near-optimal I/O efficiency. Prior B+-tree-based designs are either parallel but purely theoretical, with no high-performance implementation, or concurrent indexes such as the Bw-tree and Masstree, which run an order of magnitude slower on batch updates. We present PaB-tree, the first batch-parallel B+-tree with guarantees on work, span, and cache complexity alongside strong practical performance. Its core challenge -- repairing node overflows and underflows without eroding the tree's I/O advantage -- is resolved by one simple invariant: a repair never touches a sibling and is always pushed to the parent. A Promote primitive reduces batch construction and insertion to repeated node promotion, and batch deletion to reinsertion. Batch updates take O(B log_B n) work and O(log_B n) I/O per element, matching the sequential B+-tree bounds, with polylogarithmic span. Against highly-optimized parallel and concurrent baselines, PaB-tree delivers the best overall performance trade-off: up to 1.4x faster on construction and up to 3.6x faster on batch insertion than the strongest baseline, while preserving B+-tree query efficiency.

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