Brown eggs included by lout (4)
I believe the answer is:
boor
'lout' is the definition.
(thesaurus)
'brown eggs included' is the wordplay.
'brown' becomes 'br'.
'eggs' becomes 'oo' (visually resembles two eggs).
'included' is an insertion indicator.
'br' placed around 'oo' is 'BOOR'.
'by' is the link.
(Other definitions for boor that I've seen before include "Crude uncouth person" , "Rude, uncultivated person" , "Coarse, ill-mannered person" , "Rude, uncultured type" , "oik" .)