Yes, she is challenging him, pushing him. This is part of the negotiation within the confines of the system. She cannot outright say "hey, don't you think it would be nice to make me a cheeseburger?" Because the rules of the world demand a different behaviour. Saying that would "break the spell" so to speak, for the same reason that she can ask to get a burger to go, but she would not be able to ask "hey man aren't you happy I reconnected you with your love of cooking? Please let me go now."
This also couples with the fact that she is an escort. She is just as much performing her labour in that moment as he is performing his. She is playing the role of a customer in order to give him satisfaction. Wether he rekindles her love for her work as she does for him, I cannot say.

As soon as she mentions a cheeseburger he is happy, but they must dance this dance in order to get it. It's not about proving he's good at cooking food - It's about enjoying cooking food, hence the "with love" instead of "tasty" or "fancy" or "perfect" or "beautiful" or any other adjective that could signify quality. He accepts the task because he wants to reconnect with cooking. Look at how he behaves thru the ordering process. It takes him back, it reminds him.

Edit: thank you for your response explaining how you got that read of the situation however. I can now understand how you could have interpreted the scene as you did. Responding with a link to the scene didn't do that, so I'm glad you followed up.