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 heuristics requires substantial engineering effort, and even when implemented, these heuristics often cannot take into account semantic correlations in queries and schemas that could enable better physical plans. Using our DBPlanBench harness for the DataFusion engine, we expose the physical plan through a compact serialized representation and let the LLM propose localized edits that can be applied and executed. We then apply an evolutionary search over these edits to refine candidates across iterations. Our key insight is that LLMs can leverage semantic knowledge to identify and apply non-obvious optimizations, such as join orderings that minimize intermediate cardinalities. We obtain up to 4.78$\times$ speedups on some queries and we demonstrate a small-to-large workflow in which optimizations found on small databases transfer effectively to larger databases.