Ты мне снишься каждую ночь.
I get that ты is the subject, but to my English-speaking mind, the person dreaming is the one performing the action, and so the person dreamt about should be the object.
What is a good way to explain this usage to an English-speaking person?
The closest I can get is: "You came to me in a dream". In this case, "dream" ceases to be a verb so the translation is not exactly verbatim.