Into a bowl sift together the flour, the salt, and the cayenne, blend in the 6 tablespoons butter and the Cheddar, and stir in the cream, stirring until the mixture forms a dough. Chill the dough, wrapped in wax paper, for 2 hours.
Roll out the dough 1/16 inch thick on a lightly floured surface and using a 1 1/2 inch round cutter cut out rounds, rerolling the scraps and cutting out additional rounds. Arrange the rounds on baking sheets, brush them lightly with the egg, and bake them in batches in the middle of a preheated 450 F. oven for 5 to 7 minutes, or until they are browned lightly. The pastry rounds may be made 2 days in advance and kept in an airtight container.
In a small bowl cream together well the Swiss cheese and the remaining 3 tablespoons butter. Arrange half the pastry rounds, bottom sides up, on baking sheets, divide the cheese mixture among them, and sandwich the mixture with the remaining pastry rounds, pressing the rounds together lightly. Bake the croutes in the preheated 450 F. oven for 4 minutes, or until the cheese is just melted. Makes about 46 croutes.