Много моркови. (Genitive singular)
Много usually takes genitive plural: много огурцов (cucumbers are countable), много овощей (vegetables are countable), много яиц (eggs are countable).
But some nouns are what is called "mass nouns", and they are never used in plural. In this case, "много" takes the genitive singular:
много моркови, много картофеля, много капусты etc. It is the same as много воды (молока, сахара) etc.
Unfortunatelly, there is no rule of thumb when applying to vegetables and fruit. Some of them countable, others are not. It is just due to the tradition how people are accustomed to speak.
Some counter examples for you, Valda:
in English, "hair" is a mass noun: He has dark hair.
In Russian,"волос/волосы" is countable: У него тёмные волосы.
In English, "fruit" is a mss noun: There is a lot of fruit on the plate.
In Russian, "фрукт/фрукты" is countable: На тарелке много фруктов.
Совет (advice) is also countable in Russian: один совет, два совета, ..., много полезных советов.
And do not try to find any logic in it![]()