In a bowl stir together chutney, Cheddar, sour cream, cream cheese, and salt and pepper, to taste, until combined well.
Make 6 sandwiches with filling and bread, pressing together gently. With a 1 1/2-inch round cutter, cut 4 rounds from each sandwich.
Put coriander on a small plate and spread edges of rounds with mayonnaise to coat well. Roll edges in coriander. Sandwiches may be made 2 hours ahead, wrapped in plastic wrap, and chilled.