We present ShopTalk, a multi-turn conversational faceted search system for shopping that is designed to handle large and complex schemas that are beyond the scope of state of the art slot-filling systems. ShopTalk decouples dialog management from fulfillment, thereby allowing the dialog understanding system to be domain-agnostic and not tied to the particular shopping application. The dialog understanding system consists of a deep-learned Contextual Language Understanding module, which interprets user utterances, and a primarily rules-based Dialog-State Tracker (DST), which updates the dialog state and formulates search requests intended for the fulfillment engine. The interface between the two modules consists of a minimal set of domain-agnostic intent operators, which instruct the DST on how to update the dialog state. ShopTalk was deployed in 2020 on the Google Assistant for Shopping searches.