I would like to ask how people who are familiar with English interpret these sentences regarding the nouns that can be both count and noncount nouns.
(1) I have to make more cake/cakes to offer a wide variety of bakery products for my own business.
(2) France is famously known for having more cheese/cheeses than there are days in the year.
My foreign teachers went for plural noun in (1), but they chose the bare form for (2). I have them chose only one form for each item. For me (I’m Thai), I just want some explanations because both items represent “a variety of sth”, so why these two are treated differently.
As you note, these nouns (cake and cheese) can be both countable and non-countable. So, if you said:
I have to make more cake.
you would be using the non-countable form and the meaning is I have to make some quantity of cake. That is, you have some cake and need more. It’s not a specific amount nor is it — and this is the important part — distinct pastries. Perhaps you were having a party and you had a cake and a pie and some ice cream for dessert, but everyone wanted the cake. You find yourself running out of the cake (as a dessert choice) so you need to make more cake.
Now consider this:
I have to make more cakes.
Here you are using the countable noun and referring to multiple, distinct cakes. You might make a chocolate cake and a strawberry cake and a German chocolate cake, which would be three distinct cakes.
Similarly, when it comes to the French and their cheese, if you were talking about the aggregate amount of cheese they have (apparently a rather large amount), you would say:
France is famously known for having more cheese than there are days in the year.
But you could also be talking about the many types of cheese they have, so you would say:
France is famously known for having more cheeses than there are days in the year.
In the first case, they have a lot of cheese — it’s all lumped together. In the second, they have a lot of different types — stilton, cheddar, swiss, etc.