Preheat oven to 375 degrees F.
With a rolling pin flatten each slice of bread and with a 2 1/4-inch round cookie cutter stamp out 2 rounds from each slice. With the rolling pin flatten the rounds, brush them with butter, and fit them into 36 buttered 1/8-cup gem tins. Brush the bread with the melted butter and bake the shells in the oven for 6 minutes, or until they are pale golden. Cool the shells in the tins on cooling racks for 5 minutes, then remove the shells from the tins, and let them cool completely on the racks.
Make the filling: In a saucepan melt the butter over moderate heat, add the flour, and cook the mixture over moderately low heat, whisking, for 2 minutes. Add the half-and-half in a stream, bring the mixture to a boil, whisking, and simmer the mixture over moderately low heat, whisking for 3 minutes. Remove the pan from the heat, add the Cheddar, ham, and mustard, and season with cayenne and salt, to taste, and stir the mixture until it is combined well.
Spoon 1/4 teaspoon of the chutney into each shell and top the chutney with a rounded teaspoon of the cheese mixture. Arrange the filled shells on a jellyroll pan and freeze them for about 30 minutes or until the filling is just firms to the touch. Transfer the shells to reseal-able freezer bags, arranging them in 1 layer. Seal the bags, pressing out the air, and freeze the bites for up to 1 month.
To reheat: Arrange the shells on a baking sheet and sprinkle them with the additional Cheddar. Bake the bites in a preheated 375 degree F oven for 15 to 20 minutes, or until the filling is heated through. Run the bites under a preheated broiler about 4 inches from the heat for 30 seconds to 1 minute, or until the tops are golden.