In a small bowl, stir together the mayonnaise, 2 tablespoons of the parsley, and tarragon. Season with lemon juice, if using, hot sauce, salt, and pepper, to taste.
Spread 1 side of the bread slices with the mayonnaise mixture, arrange the onion slices evenly on half the bread slices, and top them with the remaining bread slices. Press the sandwiches together gently, trim the crusts, and cut the sandwiches into quarters.
Put the remaining 1/2 cup parsley in a shallow bowl and dip the edges of the sandwich quarters in the parsley.