Roll the slices of toast slightly thinner with a rolling pin.
Finely chop the parsley. Combine the cream cheese, mustard and parsley is a small bowl, season. Spread the cream cheese over the slices of toast.
Cut the carrot and cucumber into batons the length of a slice of toast. Remove the lettuce leaves, place on top of the cream cheese along with the carrot and cucumber batons. Cut the baking paper into strips. Roll up the toast with the filling, hold together with baking paper and kitchen twine.