Preheat the oven to 475 degrees F.
Into a medium mixing bowl, sift the self-rising flour, cake flour, baking powder, baking soda, salt and sugar. Using your fingers or a pastry cutter, work the butter into the flour until there are no butter pieces larger than a pea. Add the heavy cream to the flour mixture and, using your hands or a rubber spatula, stir just until the cream and flour come together to form a dough. Sprinkle some of the all-purpose flour on a flat surface and place the dough on top of the flour. Using your hands, press the dough into a 1/2-inch thick disk about 8 inches in diameter. Using a 3-inch round cutter dusted in flour, cut the dough into circles. Be sure to press straight and downward when cutting the dough -- a twisting motion will prevent the dough from rising. You will need to reform the scraps of dough in order to have 8 biscuits. Do this by pushing the scrap pieces together and press to reform into a 1/2-inch thick disk. Place the biscuits on a small sheet pan and brush the tops with the melted butter. Bake in the oven for 10 to 12 minutes, or until golden brown. Allow to cool briefly and serve while still warm.
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