Extremely enormous urge to have egg and coffee (8)
I believe the answer is:
espresso
'coffee' is the definition.
(espresso is a kind of coffee)
'extremely enormous urge to have egg' is the wordplay.
'extremely' suggests removing the centre (only the extremes of the word are used).
'urge' becomes 'press' (synonyms).
'to have' means one lot of letters go next to another.
'egg' becomes 'o' (an 'o' resembles an egg).
'enormous' with its middle taken out is 'es'.
'es'+'press'+'o'='ESPRESSO'
'and' acts as a link.
(Other definitions for espresso that I've seen before include "Drinks machine" , "Barista's beverage" , "strong drink" , "Strong coffee made with steam machine" , "Coffee made by forcing steam through grounds" .)