Lay out slices of white bread and flatten them with a rolling pin. Using a 2 1/4 inch round cookie cutter stamp out two rounds per slice and flatten again with rolling pin. Fit them into a mini-muffin baking tin.
Brush the bread with 4 tablespoons of melted butter. Bake the shells in a 375°F oven for 6 minutes or until they are a pale golden color. Cool on racks for 5 minutes in tins and then remove the shells from tins and let them cool completely on racks.
In a saucepan melt the remaining butter over moderate heat. Add the flour and whisk for 2 minutes. Add half-and-half cream in a stream whisking to incorporate. Add cheddar cheese, finely diced smoked ham, Dijon mustard, cayenne pepper. Stir until it is combined well.
Spoon 1/4 teaspoon mango chutney into each shell. Top with cheese mixture and smooth into a mound. Bake on a sheet pan for 15 to 20 minutes in a 375°F oven. Run the bites under the broiler for 30 seconds until the tops are golden.