Serverless computing promises fine-grained elasticity and operational simplicity, fueling widespread interest from both industry and academia. Yet this promise is undercut by the cold setart problem, where invoking a function after a period of inactivity triggers costly initialization before any work can begin. Even with today's high-speed storage, the prevailing view is that achieving sub-millisecond cold starts requires keeping state resident in memory. This paper challenges that assumption. Our analysis of existing snapshot/restore mechanisms show that OS-level limitations, not storage speed, are the real barrier to ultra-fast restores from disk. These limitations force current systems to either restore state piecemeal in a costly manner or capture too much state, leading to longer restore times and unpredictable performance. Futhermore, current memory primitives exposed by the OS make it difficult to reliably fetch data into memory and avoid costly runtime page faults. To overcome these barriers, we present Spice, an execution engine purpose-built for serverless snapshot/restore. Spice integrates directly with the OS to restore kernel state without costly replay and introduces dedicated primitives for restoring memory mappings efficiently and reliably. As a result, Spice delivers near-warm performance on cold restores from disk, reducing latency by up to 14.9x over state-of-the-art process-based systems and 10.6x over VM-based systems. This proves that high performance and memory elasticity no longer need to be a trade-off in serverless computing.