Hot partition mitigation

Design hot-partition mitigation for a DynamoDB-style key-value store where a few celebrity entities (a viral post, a flash-sale SKU) receive 100x the traffic of an average partition, causing throttling on those partition keys while the cluster is mostly idle. Writes are 30k/sec aggregate but spike to 50k/sec on a single key. How do you detect, spread, and absorb the hot key without over-provisioning everything?