Recent advances in Large Language Models (LLMs) have led to widespread adoption of third-party inference services, raising critical privacy concerns. In this work, we introduce a novel reconstruction technique that can recover original prompts from hidden states with nearly perfect accuracy across multiple state-of-the-art LLMs in the increasingly important open-weights setting. Although the attack is conceptually simple, it has not -- to the best of our knowledge -- previously been described nor shown to work practically. Furthermore, our attack remains effective against various permutation and noise-based defenses, challenging assumptions about the security of previously proposed schemes. To address these vulnerabilities, we propose Cascade, a multi-party inference scheme that leverages sharding in the sequence dimension to retain privacy of the user input. Through theoretical analysis and empirical evaluation, we demonstrate that Cascade is secure against both our attack as well as previous methods, while maintaining computational and communication efficiency. Our findings highlight the importance of rigorous security analysis in privacy-preserving LLM inference and offer practical solutions for secure deployment.