1. Slice the brioche across in pieces about one-quarter inch thick; there should be about five slices from each brioche. Cut the slices into rounds with a small biscuit cutter, about one inch in diameter
2. Choose small onions and slice them so that each circle will be a little smaller than the brioche rounds.
3. Spread each piece of brioche with mayonnaise. On half the pieces arrange one onion slice and season with salt. Cover the onion with the remaining pieces of brioche to make sandwiches.
4. Spread the remaining mayonnaise on a wooden board and sprinkle the chopped parsley on another board. Hold each sandwich lightly between thumb and finger so it will turn like a wheel. Roll the edge in mayonnaise, then in parsley. Set the sandwiches, as they are completed, on waxed paper and chill thoroughly.