One potential solution to help people change their eating behavior is to develop conversational systems able to recommend healthy recipes. Beyond the intrinsic quality of the recommendations themselves, various factors might also influence users? perception of a recommendation. Two of these factors are the conversational skills of the system and users' interaction modality. In this paper, we present Cora, a conversational system that recommends recipes aligned with its users? eating habits and current preferences. Users can interact with Cora in two different ways. They can select predefined answers by clicking on buttons to talk to Cora or write text in natural language. On the other hand, Cora can engage users through a social dialogue, or go straight to the point. We conduct an experiment to evaluate the impact of Cora's conversational skills and users' interaction mode on users' perception and intention to cook the recommended recipes. Our results show that a conversational recommendation system that engages its users through a rapport-building dialogue improves users' perception of the interaction as well as their perception of the system.