Abstract: Cloud-native LLM serving frameworks have made deployment routine in data centers, yet deploying them on leadership-class supercomputers remains an engineering challenge requiring scheduler integration, MPI launch, accelerator selection, node-local weight staging, and platform-specific patches. We present \textit{ExaServe}, a pip-installable framework that transforms a declarative YAML specification into a reproducible large-scale LLM serving deployment. Using ExaServe, we deploy LLM serving on ALCF Aurora from 1 to 256 nodes (3072 vLLM replicas). Non-streaming inference scales nearly linearly to 256 nodes, reaching 27.1\,k requests/s (3.8\,M tokens/s). Token streaming scales differently: a centralized proxy plateaus at $\sim$4.7\,k requests/s despite the model servers remaining within the service-level objective. We also identify an \emph{O}(\emph{N}\textsuperscript{2}) Ray Serve control-plane bottleneck that increases cluster bring-up to $\sim$30 minutes at 256 nodes. ExaServe provides a practical, reproducible deployment path while exposing key barriers to future exascale LLM serving.