Is Cabbage a Countable Noun?

... So from your list, onions and cabbages clearly are countable. Trouble is that when the onions and cabbages are cooked, they may become uncountable. ... Not just cooked foods but prepared, e.g. chopped onions, sliced cabbage.

Is vegetable a countable noun?

“Vegetables” is simply a countable noun.

Which type of noun is cabbage?

cabbage used as a noun:

An edible plant (Brassica oleracea var. capitata) having a head of green leaves. The leaves of this plant eaten as a vegetable. "Cabbage is good for you."