Peer-counseling is essential in online mental health communities to provide relatable support to those seeking help, but the peer-counselors often lack professional training in therapeutic counseling to produce the desired cognitive changes. In this paper, we present STEPS, an AI-powered assistive dialog tool for peer-counseling. Unlike other existing tools, STEPS assists peer-counselors in facilitating cognitive change in online counseling settings. Towards this goal, we emulate two key phases in a Schema Therapy-based in-person counseling session–(1) Schema Assessment to uncover the deep-seated irrational beliefs underlying an individual’s mental health problems, and (2) Cognitive Change to reframe these beliefs into healthier alternatives. In both phases, we employ Socratic questioning techniques to effectively elicit critical introspection and guide cognitive change. We describe STEPS and present expert evaluation studies on its counseling conversations on real-world mental health forum posts. Our results indicate that STEPS significantly outperforms competitive baselines on all key metrics related to schema assessment, cognitive change strategies, and critical thinking, achieving an impressive average rating of 5 out of 6, highlighting its strong potential as a transformative tool for online peer-counseling.