It is about cheese. Asking for cheese is a very minor and reasonable request.
What would I do as an adult if I wanted more cheese on my pasta? I'd go and get myself some. Cheese and pasta is delicious. You can see how many adults agree that they'd give more cheese on this thread. If it doesn't make sense to an adult, it is definitely not going to make sense to a six year old.
Denying reasonable requests can cause children to become very angry, because they need the world to feel just.
Yes, there's an issue with screaming for cheese and it's completely unacceptable. And no, of course you can't give in to that kind of behaviour. But you need to pick your battles, particularly where food is concerned. If you make a child feel like they have no autonomy and that they're subject to completely arbitrary rules, it's not surprising that they become emotional about it.
I suspect this child feels like she's not being listened to. And what's the obvious solution to no one listening to you, when you're six? Make your request louder. It's easy to follow her logic.
Then she's being told she's being punished further with something that again makes no sense. Days into the future, which is a long time into the future for a young mind, she's not allowed her friends over. Again, it makes no sense, she becomes angry, she feels like she's out of control of her life, she can't regulate her emotions at that age, she knows eventually someone will listen if she shouts long enough, and here we are.
She doesn't sound like a little madam. She sounds like she's trying to navigate life's difficulties the best way she knows how.
And all this over 30 pence of cheese.