Who (if anyone) is the narrator (Montresor) talking to at the end of "The Cask of Amontillado"?

There are several possible answers to this. Some argue that he is writing his confession, rather than speaking it, and that it is addressed to whomever finds it. In this case, Montresor would not have a specific audience in mind. We already know he is an unreliable narrator, and this might be magnified if he didn't know the person to whom he was relating his story.

However, he does state that the one to whom he is speaking knows "the nature of [his] soul." Thus, it can be inferred that he is well-acquainted with his audience. If this is the perspective you wish to take, it would follow that Montresor either absolutely believes what he's saying, or that he needs his audience to believe that he was justified in his actions. Therefore, he intimates that the reader knows his soul, and brings us into his confidence, attempting to convince both us and himself of the righteousness of his actions.