Burden in French Canada at first, cooking cream bun (11)
I believe the answer is:
encumbrance
'burden' is the definition.
('encumbrance' can be a synonym of 'burden')
'in french canada at first cooking cream bun' is the wordplay.
'in french' becomes 'en' ('en' can be French for 'in' e.g. en France).
'at first' indicates taking the first letters.
'cooking' indicates anagramming the letters.
The first letter of 'canada' is 'c'.
'cream'+'bun'='creambun'
'creambun' with letters rearranged gives 'umbrance'.
'en'+'c'+'umbrance'='ENCUMBRANCE'
(Other definitions for encumbrance that I've seen before include "confounded nuisance!" , "drag" , "Impediment - burden" , "liability" .)