Slice the brioche bread into fingers. Whisk together the eggs, milk and vanilla extract.
On a separate plate, mix together the sugar and cinnamon.
Heat the butter in a large frying pan. Briefly dip the bread sticks in the egg mixture, turning to coat and place in the frying pan. Fry on all sides until golden brown, then immediately transfer to the cinnamon sugar. Roll the fried bread sticks in the cinnamon sugar.