Automating Infrastructure-as-Code (IaC) is challenging, and large language models (LLMs) often produce incorrect configurations from natural language (NL). We present TerraFormer, a neuro-symbolic framework for IaC generation and mutation that combines supervised fine-tuning with verifier-guided reinforcement learning, using formal verification tools to provide feedback on syntax, deployability, and policy compliance. We curate two large, high-quality NL-to-IaC datasets, TF-Gen (152k instances) and TF-Mutn (52k instances), via multi-stage verification and iterative LLM self-correction. Evaluations against 17 state-of-the-art LLMs, including ~50x larger models like Sonnet 3.7, DeepSeek-R1, and GPT-4.1, show that TerraFormer improves correctness over its base LLM by 15.94% on IaC-Eval, 11.65% on TF-Gen (Test), and 19.60% on TF-Mutn (Test). It outperforms larger models on both TF-Gen (Test) and TF-Mutn (Test), ranks third on IaC-Eval, and achieves top best-practices and security compliance.