This study proposes a cognitive benchmarking framework to evaluate how large language models (LLMs) process and apply culturally specific knowledge. The framework integrates Bloom's Taxonomy with Retrieval-Augmented Generation (RAG) to assess model performance across six hierarchical cognitive domains: Remembering, Understanding, Applying, Analyzing, Evaluating, and Creating. Using a curated Taiwanese Hakka digital cultural archive as the primary testbed, the evaluation measures LLM-generated responses' semantic accuracy and cultural relevance.