The way you introduce an object in your source code will lead Inform to decide whether it is singular or plural. But in addition to that, you can just tell Inform whether it is singular or plural, or change the indefinite article for it. This is discussed in 3.18 of the documentation, with the ‘some water’ example. This example matches your cheese situation.
Create the cheese with “the”. e.g. “the cheese is on the table.” This makes sure the cheese is single-named. But you may not want Inform to then talk about “the” cheese. The preferred article is “some”. So you can then just tell Inform what you want the article to be:
the cheese is on the table. The indefinite article of the cheese is "some".
What you call an ‘uncountable’ noun needs to be set up in Inform as single-named, and then you modify its indefinite article. If it was plural-named, you would end up with mistakes like:
>EAT CHEESE
The cheese are tasty.
-Wade