Many real-world conversational settings for knowledge discovery, including podcasts, hiring screens, and marketplaces, require a purpose-driven understanding of a person. We study the Next-Best-Question (NBQ) problem: at each turn, an interviewer should ask the question with the highest expected information gain given what has already been learned and the conversation goal. We propose NBQ, a plug-and-play framework that seeds a diverse pool of candidate questions, maintains a compact and continuously updated user state, adaptively selects the next question within a turn budget, and distills the resulting free-form dialogue into a structured vector-based user profile. As a demanding application, we instantiate NBQ for reciprocal matchmaking, where compatibility must be mutual and each person is modeled by both self-description and counterpart-preference representations. To support large-scale matching, we further introduce QuickMatch, an efficient retrieval layer that recasts reciprocal matching from quadratic pairwise scoring to approximate vector search. Experiments show that NBQ improves user profiling quality by up to 13.6% and 14.0% in AC@T and AR@T, respectively, while QuickMatch accelerates retrieval by up to 22.9x with recall up to 0.989.