Speech Event Extraction (SpeechEE) is a challenging task that lies at the intersection of Automatic Speech Recognition (ASR) and Natural Language Processing (NLP), requiring the identification of structured event information from spoken language. In this work, we present a modular, pipeline-based SpeechEE framework that integrates high-performance ASR with semantic search-enhanced prompting of Large Language Models (LLMs). Our system first classifies speech segments likely to contain events using a hybrid filtering mechanism including rule-based, BERT-based, and LLM-based models. It then employs few-shot LLM prompting, dynamically enriched via semantic similarity retrieval, to identify event triggers and extract corresponding arguments. We evaluate the pipeline using multiple LLMs (Llama3-8B, GPT-4o-mini, and o1-mini) highlighting significant performance gains with o1-mini, which achieves 63.3% F1 on trigger classification and 27.8% F1 on argument classification, outperforming prior benchmarks. Our results demonstrate that pipeline approaches, when empowered by retrieval-augmented LLMs, can rival or exceed end-to-end systems while maintaining interpretability and modularity. This work provides practical insights into LLM-driven event extraction and opens pathways for future hybrid models combining textual and acoustic features.