This is the 10009th most frequent Polish word.
badawczej
"Badawczej" means "research" or "investigative" (adjective form).
In this sentence, "badawczej" is an adjective form describing the style of narration (investigative).
Książka była napisana w stylu badawczej narracji.
The book was written in the style of investigative narrative.
Here, "badawczej" modifies "methodology" and pertains to its function related to research.
Pracujemy nad rozwojem naszej badawczej metodologii.
We are working on developing our research methodology.
In this context, "badawczej" describes the type of work being undertaken (investigative or research-oriented).