Social media platforms play a pivotal role in shaping political discourse, but analyzing their vast and rapidly evolving content remains a major challenge. We introduce an end-to-end framework for automatically inducing an interpretable topic taxonomy from unlabeled text corpora. By combining unsupervised clustering with prompt-based inference, our method leverages large language models (LLMs) to iteratively construct a taxonomy without requiring seed sets (predefined labels) or domain expertise. We validate the framework through a study of political advertising ahead of the 2024 U.S. presidential election. The induced taxonomy yields semantically rich topic labels and supports downstream analyses, including moral framing, in this setting. Results suggest that structured, iterative labeling yields more consistent and interpretable topic labels than existing approaches under human evaluation, and is practical for analyzing large-scale political advertising data.