Preheat oven to 450 degrees F. Line a baking sheet or round cake pan with parchment paper; set aside.
In a large bowl, sift together flour, baking powder, baking soda, salt and sugar. Use a pastry cutter or two forks to cut the butter and shortening into the flour mixture until incorporated and the mixture resembles coarse meal. You will still see flakes of butter and shortening throughout, which is good!
Gradually add the buttermilk, stirring with a wooden spoon until a fairly wet, sticky dough forms. Turn out onto a lightly floured surface and knead for about 1 minute, adding flour to the counter and your hands, as necessary, to prevent sticking. Roll or pat to ¾-inch thickness. Use a small biscuit cutter to cut out rounds (I recommend a 2-inch cutter or smaller for ham biscuits). Firmly press the cutter down into the dough, but do not twist. Twisting the biscuit cutter seals off the edges of the biscuits and they therefore will not rise as high.
Arrange biscuits (with sides touching) on the parchment-lined baking sheet or round pan. Brush the tops of the biscuits with a little bit of the melted butter. Place the tray of biscuits in the refrigerator for about 5 minutes (if you have time) to chill before popping them in the oven.
Bake for 10-12 minutes, or until tops are golden brown. Brush the tops with additional melted butter, transfer to wire rack to cool slightly, and assemble sandwiches.