When looking for synonyms for the phrase "thought-provoking analysis", there are a few options that you can consider. Firstly, "critical examination" is a phrase that can be used to imply a deep and thoughtful analysis of a subject. "Insightful scrutiny" is another option that suggests an in-depth investigation that reveals key insights. "Reflective evaluation" can also be used to describe an analysis that encourages deeper contemplation and introspection. "Intellectual investigation" is another phrase that can be used to describe an analysis that involves a high level of intellectual rigor and thoughtfulness. Ultimately, the right synonym will depend on the broader context and the intended tone and focus of the analysis.