Nut with piece of cake, but different starter (6)
I believe the answer is:
Here is my best explanation:
'nut' is the definition.
'piece of cake but different starter' is the subsidiary indication.
I cannot quite see how this works, but
'piece' could be 'n' (abbreviation for Knight in chess notation) and 'n' is present in the answer.
'of' could be 'o' and 'o' is present in the answer.
'starter' could be 'l' and 'l' is present in the answer.
This explanation may well be incorrect...
'with' is the link.
(Other definitions for noddle that I've seen before include "Jocular word for head", "Bonce", "bonce", "Head (sl.)" and "Head or brain (slang)".)