Better cook the eggs in with the vegetable (8)
I believe the answer is:
beetroot
'the vegetable' is the definition.
(beetroot is a kind of vegetable)
'better cook the eggs in' is the wordplay.
'cook' indicates anagramming the letters.
'the eggs' becomes 'oo' (visually resembles two eggs).
'in' indicates putting letters inside.
'better' is an anagram of 'beetrt'.
'beetrt' going around 'oo' is 'BEETROOT'.
'with' acts as a link.
(Other definitions for beetroot that I've seen before include "vegetable's produced" , "Food" , "plant" , "Vegetable cooked or used in salads and pickles" , "Essential ingredient in borsch" .)