I try and separate children's requests into two categories. Things they've asked for that seem unusual but are actually harmless and things that really are unreasonable requests.
For example, mummy can we go and look in that bin? (This is a real example). My first thought was of course not. But actually it's safe, it's harmless, it doesn't cost money or involve a huge investment of time and energy. So my answer was yes, we can look in the bin to see what's in there.
Same with stuff like, can I watch the same episode of the same programme ten times in a row, can I go and stand in that puddle (in sensible shoes), can I put stickers on my face etc.
I'd class the cheese request in that category. Unless there's a particular reason why she shouldn't be allowed to eat cheese or it's becoming an excessive amount of cheese, I really don't see the harm in it. I sometimes go and grate myself some more cheese for pasta.
So, ask yourself is it dangerous, is it reasonable?
When it is dangerous or it is genuinely unreasonable, you explain very clearly the rationale behind your decision. Children like things to make sense. They have a strong sense of unfairness. So you can just take things away or punish them unless it's clear why it's happening.
Don't just say no. Explain why it isn't a good idea.
When the answer is no, you never ever go back on that. I don't need to explain what happens if you show that your word is inconsistent.
Keep saying no, keep explaining yourself. Remain empathetic. You can say things like, I appreciate this isn't what you wanted and it's upsetting for you. But don't get emotional. Don't shout. Don't show that you're stressed or at breaking point. Keep calmly saying no and explaining why.
It might be that you need to spend a while on this to break this habit but eventually the message will get through.