Classroom discourse profoundly shapes student learning, yet analyzing teacher talk at scale remains challenging in non-Western and low-resource language contexts. This paper introduces CantoTalk, a dataset of 7,518 Cantonese teacher utterances from Hong Kong mathematics classrooms annotated with ten talk-move categories. We investigate whether LLMs can reliably classify these moves and encode systematic differences in teacher expertise. Fine-tuning five open-weight LLMs yields strong performance, with the best model (Qwen3-8B) achieving micro-F1 of 0.81 and macro-F1 of 0.77. Probing utterance-level embeddings reveals that teacher expertise is linearly separable with 0.79 balanced accuracy, well above chance even after controlling for surface features. Clustering analyses uncover three coherent discourse styles differing in pedagogical authority, scaffolding, and dialogic engagement, with qualitative analysis showing systematic differences in how experienced and novice teachers execute similar talk moves. These findings demonstrate that fine-tuned LLM representations capture teacher expertise, offering a new lens for analyzing classroom discourse and informing teacher feedback tools.