We might, for instance, serve
with the dessert.
Peebles [Na Pùballan] goat cheese [chèvre] and Vietnamese bread [Bánh mì] in the manner of [à la] Machiavelli [Niccolò]
Paraguayan [Guaraní] artist Joan [Miró] Castro’s [Raúl] sugar-coated [glacé] shark dish [Kæstur hákarl].
Childlike [naïve] author Charlotte [Brontë] Hitler’s [Führer] sour herring [Surströmming] and ...
each course has one of each vowel suitably accented -- but the original version of the puzzle had fewer items on each line, so I'm not sure whether that's explicitly intended to be a constraint or not. Either way, my answer respects the constraint.
Credit where due:
NudgeNudge spotted Guaraní. Fillet spotted Raúl. Thanks! (Reader, if you liked this answer, consider finding something of theirs and voting it up.)