Abstract: Machine learning (ML) increasingly powers Internet of Things (IoT) applications at the edge. Yet producing a deployable edge ML artifact for a specific scenario requires navigating a huge search space spanning data representation, model design, training on domain-specific data, and runtime customization. This workflow is fragmented and difficult to scale across diverse edge applications. We present EdgeCraft, an LLM-driven system that turns high-level intent into deployable edge ML artifacts. Building such a system raises two challenges: (1) How can an LLM be guided to find high-quality solutions that meet dynamic SLOs for task quality, latency, and energy? (2) How can trustworthy target-device verification be obtained at low cost? EdgeCraft addresses these challenges with two designs. (1) A constraint-aware synthesis tree explores alternative candidates and uses measured SLO gaps to guide each improvement. (2) A multi-fidelity verifier progressively combines low-cost checks with full target-device verification to reduce verification cost while preserving reliable verification results. It also records verified failures for reuse, avoiding repeated device work. To support concurrency, EdgeCraft provides a multi-tenant runtime that runs cloud training and target-device verification in parallel while isolating requests. Across 50 public tasks, EdgeCraft exceeds the task-specific Reference in best-observed quality on 40 tasks and finds an SLO-feasible artifact on 45, with the two outcomes overlapping on 38 tasks. Moreover, EdgeCraft achieves competitive performance on our self-collected SEN dataset, suggesting its generalizability to real-world IoT sensing tasks.