Stir together cream cheese and mayonnaise. Stir in chicken and next 7 ingredients. Cover and chill at least 4 hours.
Cut bread slices with assorted 2 1/2-inch cutters, reserving trimmings for other uses. Spread half of bread shapes with chicken mixture; top each with a matching bread shape. Roll sandwich edges in parsley, if desired.
Note: To make finger sandwiches, cut crusts from 42 bread slices (about 2 loaves). Spread half of slices with filling; top with remaining bread slices. Cut each sandwich into 4 equal strips. Roll edges in parsley, if desired.