Traditional query optimization relies on cost-based optimizers that estimate execution cost (e.g., runtime, memory, and I/O) using predefined heuristics and statistical models. Improving these requires substantial engineering effort, yet they often cannot exploit semantic correlations in queries and schemas that could enable better physical plans. Large language models (LLMs), however, can reason about column semantics, value distributions, and broader domain context that classical statistics miss. We introduce DBPlanBench, a harness for the DataFusion engine that exposes physical plans through a compact serialized representation and applies LLM-proposed edits as JSON patches. On this harness, we instantiate a test-time optimization workflow where an LLM examines physical query plans, proposes localized edits based on semantic reasoning, and an evolutionary search refines the candidates across iterations. We target OLAP queries, where heavy, repeated execution turns even small efficiency gains into substantial cumulative savings. We specifically focus our evaluation on join reordering and join-side selection, where cardinality-estimation errors compound multiplicatively. Median speedups reach $1.10$-$1.12\times$ on TPC-H and $1.05$-$1.07\times$ on TPC-DS, with some achieving up to $4.78\times$. We also demonstrate that optimizations discovered at small scale factors transfer effectively to larger ones, supporting a low-cost small-to-large workflow.