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Persistent memory (PM) brings important opportunities for improving data storage including the widely used hash tables. However, PM is not friendly to small writes, which causes existing PM hashes to suffer from high hardware write amplification. Hybrid memory offers the performance and concurrency of DRAM and the durability and capacity of PM, but existing hybrid memory hashes cannot deliver high performance, low DRAM footprint, and fast recovery at the same time. This paper proposes WALSH, a flat hash with novel log-structured separate chaining designs to optimize the performance while ensuring low DRAM footprint and fast recovery. To address the overhead of hash resizing and garbage collection (GC), WALSH further proposes partial resizing/GC mechanisms and a 4-phase protocol for concurrent hash operations. As a result, WALSH is the first flat index for hybrid memory with embedded write aggregation ability. A comprehensive evaluation shows that WALSH substantially outperforms state-of-the-art hybrid memory hashes; e.g., its insert throughput is up to 2.4X that of related works while saving more than 87% of DRAM. WALSH also provides efficient recovery; e.g., it can recover a dataset with 1 billion objects in just a few seconds.