Countable/Uncountable: vegetables

Hello,

I know that "vegetables" is usually seen in the plural form. But when we talk about cooking, should be treat the word "vegetable" as countable or uncountable noun.

a) This soup needs a few vegetables in it.
(= different types of vegetables?)

b) This soup needs a little vegetable in it.
(= a small quantity of vegetables, maybe a carrot?)

I read somewhere a long time ago that fruit and vegetables are sometimes uncountable when they are used in cooking, which is understandable since once they are chopped up, there is no telling how many they were. I remember this sentence was used as an example.

c) The stew has too much carrot.

Now I'm not so sure if what I read way back then is correct. Is it more natural to say:

d) You can add some carrots to the stew.

Or

e) You can add some carrot to the stew.

Best regards,

Naweewra