“Passes” and “serves” mean different things, when it comes to food. “Passing” the food is something that a person does when they are seated at a table with others; for example, you could pass a plate of potatoes to the person sitting next to you, so that he can take some for himself. Another example: “Please pass the soy sauce.” “Serving” the food usually means delivering food to another person. Examples: “The waitress took a long time to serve us our food.” “Please come to the table, kids. I’ll be serving dinner in just a minute.”

Alistair, put your comment in as an answer and then Mraz can choose it (if they want to) to close this question

‘She passes the cheese.’ is correct.

To pass the cheese means you give the plate of cheese to someone who can’t reach it. To serve the cheese means to provide the cheese as the host or waiter, and includes the act of bringing the cheese to the table and putting cheese on guests plates for them.